The moves buy May a temporary reprieve.
That means it will support a Conservative minority government on key votes in parliament without a formal coalition deal.
On Saturday, both Ms Hill and Mr Timothy announced their resignations.
Labour stunned even its own supporters by winning more parliamentary seats than expected and, although it lost the election, its performance was widely seen as a moral victory for Corbyn.
Now that the Conservative party is under threat of falling, the Labour party's rise seems quite probable.
Foreign Secretary Boris Johnson, Home Secretary Amber Rudd, Brexit Secretary David Davis and Defence Secretary Sir Michael Fallon will also stay where they are.
"We can confirm that the Democratic Unionist party have agreed to the principles of an outline agreement to support the Conservative government on a confidence and supply basis when parliament returns next week", a government spokesman said.
"It was a disaster", he said.
The strong showing for Labour in the election was capped when the party snatched the final seat to declare, Kensington, by just 20 votes late on Friday.
Martin Selmayr, senior aide to European Commission President Jean-Claude Juncker, responded to the resignations by tweeting the word "bauernopfer" - German for the sacrifice of a pawn in chess. May's gamble in calling an early election backfired spectacularly, as her Conservative Party lost its majority in Parliament.More news: Pres. Trump Proposes Privatizing Air Traffic Control
May called the vote three years early in the hope of scoring a sweeping win to strengthen her hand in the challenging Brexit talks, which are due to start in nine days' time.
Lord Murphy said such a deal could undermine decades of efforts to bring stability to Northern Ireland. A Downing Street spokeswoman declined to explain the discrepancy between the two.
Instead, the election ended up wiping out the Conservative majority.
The arrangement with the DUP will make governing easier, but it makes some Conservatives uneasy. The Democratic Unionist Party is a socially conservative, pro-British party known for opposing abortion and marriage equality.
Mr Corbyn says also said he would reach out to the moderate MPs in his party who had quit the Shadow Cabinet because they didn't want to serve him.
But the PM has not fully nailed down an agreement with the Northern Irish party, with its leader Arlen Foster flying to London on Tuesday to firm up a deal.
In a hint that curbing immigration could become a lower priority than safeguarding the economy she said: "It is about making sure that put free trade at the heart of what it is we seek to achieve as we leave".
Still the deal with the DUP risks upsetting the political balance in Northern Ireland.
Ms Cooper, who has been one of Mr Corbyn's fiercest Labour critics, insisted the party is now united behind the leader despite the civil war which raged between him and his MPs previous year.
"By the time we saw her finally show some emotion in the campaign it was when she fucked it all up".
"It's a very fragmented and hard time", says Evans.