The prime minister said 2030 would be the "right time" for the UK to host the games - the first time since England won it in while hosting in 1966.
Mr Johnson, speaking in an interview with the Sun newspaper, also offered to host the entire Euros competition this year, rather than just the final and semi final as planned, with the UK's coronavirus vaccine rollout steaming ahead of the rest of Europe.
On the 2030 World Cup bid, the PM said: “We are very, very keen to bring football home in 2030. I do think it’s the right place.
“It’s the home of football, it’s the right time. It will be an absolutely wonderful thing for the country.”
The English Football Association said on Twitter that it welcomed “the government’s pledge of £2.8million towards a potential bid” for the 2030 World Cup.
A joint statement released by all football associations involved in the bid, said: “The football associations and Government partners of the UK and Ireland are delighted that the UK Government has committed to support a prospective five-association bid for the 2030 FIFA World Cup."
It added: "Staging a FIFA World Cup would provide an incredible opportunity to deliver tangible benefits for our nations.
“If a decision is made to bid for the event, we look forward to presenting our hosting proposals to FIFA and the wider global football community.”
The 2022 World Cup will take place in Qatar next year, while the 2026 tournament is to be held in the United States, Canada and Mexico.
On this year's Euros, which were postponed last year due to the Covid-19 pandemic, Mr Johnson said: "We are hosting the Euros. We are hosting the semis and the final. If there’s any other matches that they want hosted, we’re certainly on for that but at the moment that’s where we are with UEFA.”
London, Glasgow and Dublin are among the 12 host cities hosting the games, though it is not yet clear whether fans will be allowed to attend all games.
If Mr Johnson's roadmap out of lockdown goes according to plan, at least 10,000 could be allowed to attend matches hosted at England's biggest stadiums, such as Wembley.
From May 17 at the earliest, the plan is to allow 10,000 fans to attend matches or 25% of the stadium's capacity, whichever is smallest.
Sticking to the roadmap depends on a number of factors, including Covid-19 vaccine rollout, with the UK aiming to have vaccinated all nine groups considered most vulnerable to the virus by mid-April.