Video report by ITV News Political Correspondent Libby Wiener
Each contender in the race was required to gain the backing of at least 33 Tory MPs in order to progress but Mr Stewart failed to do so, only gaining 27 votes - 10 less than in the previous ballot.
Boris Johnson was again well ahead of the pack with 143 votes from Tory colleagues, cementing his position as the firm favourite.
After topping the ballot for a third time, he tweeted: "Thank you once again to friends and colleagues for your support in the third ballot - especially on my birthday! We've come a long way but we have much further to go."
The results were as follows: Michael Gove, 51. Jeremy Hunt, 54. Sajid Javid, 38. Boris Johnson, 143. Rory Stewart, 27.
Speaking to ITV News after being eliminated, International Development Secretary Mr Stewart said the result was "disappointing", adding how his exit means a no deal exit is now a real option.
He said: "Now that I've left this race, I'm the only person in the race that was saying a no deal Brexit would be a bad idea, every other candidate has left no deal on the table."
He added: "Clearly, the majority of my colleagues in the House of Commons at the moment agree with them and not with me."
When asked by ITV News Political Correspondent Libby Wiener if he believed he had been the victim of "vote lending, which gave you a surge but has now eliminated you", Mr Stewart said "all sorts of things might be happening".
He added how he now plans to see his children, aged two and four, and would not commit to backing any of the remaining contenders.
Earlier in the day Mr Stewart admitted his performance in the BBC debate, which he admitted was lacklustre, "could" have knocked his support among MPs.
ITV News Political Editor Robert Peston agreed with him, writing on Twitter: "As I warned, he lost support in the debate last night by seeming to be a divisive candidate."
Asked if he was deflated following the result, Mr Stewart told Sky News: "No, I'm feeling energised: the reality is you never know what MPs get up to in a secret ballot. They clearly decided that they were going to back a winner and they're going to go in other directions."
He said he was surprised that he had lost 10 votes, and did not understand why, adding: "But something in the air must have made them sense that something was going in the other direction."
Mr Stewart also tweeted: "I am so moved & inspired by the support I have received over the last few weeks - it has given me a new faith in politics, a new belief in our country.
"I didn't get enough MPs to believe today - but they will. I remain deeply committed to you and to this country."
Following the results Jeremy Hunt told ITV News: "I'm very happy with the results because three times now the party's MPs have chosen me to be the main challenger to Boris, the front-runner.
"I am the person who is best placed to get a better Brexit deal from the EU."
When asked what more he could do to boost his changes, he said: "People have been predicting that I was going to be knocked out and each time I have exceeded expectations and that's what I intend to do tomorrow."
He also tweeted: "Three times now MPs have chosen me as the person best-paced to take on Boris.
"If I make it to the final I will put my heart & soul into giving him the contest of his life: in politics today the unexpected often happens. The stakes too high to allow anyone to sail through untested."
Sajid Javid spoke to ITV News following the results and despite being 13 votes behind third place insisted he would not be pulling out the race ahead of Thursday's ballots.
He said: "People said I was trailing yesterday and I'm still here."
He added: "What matters now is for my colleagues to decide who is the best person to be up there in the final two with Boris Johnson and I think I have an incredibly strong case."
He also tweeted: "Delighted to make it through to the final day of MP voting. Grateful for the support of many excellent colleagues. We can do this! #TeamSaj #BrexitAndBeyond
"Thank you @RoryStewartUK for the positive impact you have had on this campaign. You've injected it with real humility, authenticity, and pragmatism. Like many I look forward to seeing the contribution you will make to our party and the country in the future."
In a video posted to Twitter, Mr Gove said: "I'm delighted by today's result, so pleased to have the backing of 10 more Conservative MPs, closing the gap on second place.
"I hope tomorrow we'll be able to make it to the final two in this race and I just want to say 'thank you' to everyone who supported me.
"I'm determined to make this a contest of ideas in which we can all ensure we play our part in building a better Britain."
Justice Secretary David Gauke, who had backed Mr Stewart to win the contest admitted being "disappointed" his horse in the race had failed to progress.
He added: "It it has been a privilege to have supported him. He has been an inspirational candidate delivering a message of honesty & realism. He's now a major figure in our politics with a big role to play."
Tory MPs began voting for who they wanted to lead the party - and as a result become the next prime minister - at 3pm, with the ballot closing at 5pm.
Consistent frontrunner Boris Johnson mumbled and smiled but did not answer questions from reporters after he voted in the third ballot.
The former foreign secretary has been tipped as the favourite in the Tory leadership race right from the start, and ended the third round of voting with the same number as all three of his remaining rivals combined.
Mr Johnson was a key figure in the Vote Leave campaign during the 2016 referendum, and has committed to keeping the October 31 deadline, even if that means leaving without a deal - and has said he will step up no-deal preparations.
Aside from his high profile, humour and off-the-cuff style, it's his commitment to a swift Brexit which is likely drawing in lots of support.
The remaining MPs vying for the top job will now, unless two voluntarily drop out, face two more ballots on Thursday to whittle numbers down to the final two.
Then on Saturday June 22 will be the first hustings event for Tory members, followed by several more throughout the four weeks of campaigning before the winner is announced on the week of July 22.
As MPs were voting, ITV News Political Editor Robert Peston assessed how the contenders' claim they'll resolve Brexit, saying he'd have given them all an F grade.
He said: "If I were grading these exam papers, I am afraid I would give an "F' for fail to each of them - although Michael Gove and Rory Stewart at least have a little bit more imagination than the rest with, respectively, their suggested "union guarantee" and "Brexit Assembly".
Peston pointed out that if anyone in Europe is paying attention to the Tory leadership contest, then UK politics "will seem even more ridiculous than the England team did under Steve McClaren".
It comes after outsider Mr Stewart reached out to Michael Gove's campaign team, requesting the environment secretary join forces with him in order to defeat Boris Johnson.
Aside from the chasm that would have needed to be closed if the pair were to agree on various issues, not least Brexit, it's unlikely Mr Gove would have given in to one of Mr Stewart's more audacious demands.
A spokesman for Mr Stewart said: "Clearly at some time, people will need to combine teams.
"But any team that gets combined, Rory wants to lead it."
Despite Mr Stewart's best efforts to gain support in the race from one of the leading contenders, he was eliminated after 10 supporters jumped ship.