Video report by ITV News Political Editor Robert Peston.
Theresa May claimed her new ministerial team is more diverse and will "better reflect the country which it serves" as a result of the reshuffle, Downing Street said.
It said that there are now more women attending Cabinet, more female ministers and more members of the Government from a black and minority ethnic background than before.
The Prime Minister sacked a number of middle-ranking white, male ministers - including an MP at the centre of a sex-toy storm - and promoted younger MPs to ministerial roles.
However, social media users questioned whether Mrs May's claims of a diverse Cabinet were accurate.
Former leader of the Liberal Democrats Tim Farron said: "That wasn't a reshuffle, it was a half hearted stir, with all the useless lumpy bits unmoved in the middle."
Mrs May's latest appointments included Alok Sharma who was given the role of Employment Minister, the role rejected by former Education Secretary Justine Greening.
Mr Sharma spent just seven months as Housing Minister, a role that has now been taken by Dominic Raab, MP for Esher and Walton.
Another appointment included Suella Fernandes - leader of the influential pro-Brexit European Research Group of backbenchers - to the department responsible for the UK's departure from the EU.
The Fareham MP was elected in 2015 and is the daughter of immigrants from Kenya and Mauritius.
Casualties of the reshuffle included Mark Garnier, who said he was "very sad" to lose his job as trade minister.
Last month, an investigation found Mr Garnier did not breach ministerial code over allegations of inappropriate behaviour towards a female member of staff, including asking her to buy a sex toy.
After the conclusion of a Cabinet Office investigation into the allegations, Mrs May said that "a line should be drawn under the issue" and on Tuesday No 10 sources insisted the incident had nothing to do with his departure.
Other casualties included Robert Goodwill, who lost his role as Children and Families Minister, Philip Dunne who was removed as health minister and John Hayes who resigned from the Department of Transport.
Tory backbencher Philip Davies, who sits on the Commons Women and Equalities Committee, said the reshuffle had created "a legitimate concern that some people may feel they have been hoofed out or not promoted simply because they are a white male".
He told The Daily Telegraph: "It certainly does not do anyone any favours to promote people who are not ready for promotion just because of their gender or race."
But the Prime Minister's official spokesman said: "It is about getting the right Government in place to deliver for the British public.
"That also includes delivering a Government that better reflects the country which it serves."
In further appointments, Jo Johnson MP, brother to Foreign Secretary Boris Johnson, has been made Transport Minister and Minister for London.
And Sam Gyimah, Prisons and Probation Minister and MP for East Surrey, was made Universities Minister.
However, the Cabinet's "big four" - Chancellor Philip Hammond, Foreign Secretary Boris Johnson, Home Secretary Amber Rudd and Brexit Secretary David Davis - all remained in place.
Transport Secretary Chris Grayling, Business Secretary Greg Clark and Commons Leader Andrea Leadsom also remained in post following widespread speculation that Mrs May would demote them.
On Monday, the PM's reshuffle plans were derailed as Education Secretary Justine Greening rejected the work and pensions role and quit the Cabinet and Health Secretary Jeremy Hunt apparently refused to budge after turning down the business role.
Ms Greening said she thought it was the "right thing to do" to quit government rather than take the role at the Department for Work and Pensions (DWP).
Tory grandee Sir Nicholas Soames joined the calls for a "major improvement" on Twitter.
Monday's bungled cabinet reshuffle was underlined by the Tory press team wrongly announcing Mr Grayling as the party's new chairman only for Brandon Lewis to be appointed an hour later.
Despite widespread criticism of the shake-up, newly-appointed Tory chairman Brandon Lewis insisted the party is "not quite" in a mess but admitted there was a "job of work" to be done.
However, more negativity for Mrs May came as, outside of Cabinet, Toby Young quit his recently appointed role with the universities regulator.
His resignation came a day after the prime minister had defended the journalist and free school supporter in the role amid doubts over his lack of education experience and criticism of past comments on social media.