Under the deal, about one billion pounds (1.27 billion US dollars) in concessions have been made to Northern Ireland's largest party in exchange for support from its 10 MPs on key votes in the House of Commons.
For any other measures support would be on a vote-by-vote basis, the text of the agreement said.
The nasty party is back, propped up by the DUP.
Labour Party leader Jeremy Corbyn complained that the new deal was "clearly not in the national interest".
Conservatives insists the DUP remain an opposition party. Cooperation between Britain and European Union member Ireland lies at its heart.
Ms Sturgeon said: "In concluding this grubby, shameless deal, the Tories have shown that they will stop at nothing to hold on to power - even sacrificing the very basic principles of devolution".
The DUP was founded by the late Protestant firebrand Ian Paisley, who for decades brooked no compromise with Northern Ireland's Catholic minority before entering into an unlikely power-sharing deal with Sinn Fein. It opposes the right to abortion, which was legalized in England, Scotland and Wales in 1967.
Some of its representatives have also been criticised in the past for homophobic comments, climate-change-denial statements and sectarian rhetoric.
There is particular concern over the peace process.
May's pledge to provide the funding through the province's power-sharing executive put pressure on the pro-British DUP and Irish nationalist rivals Sinn Fein to revive their compulsory coalition before a fresh deadline to do so elapses on Thursday. The DUP - the largest party in Northern Ireland - stands against same-sex marriage and opposes the lifting of a near-total ban on abortion now in place in Ireland. With May relying on the DUP's 10 legislators to win votes in the House of Commons, talks centred on extra money for Northern Ireland and Brexit plans.
The recent United Kingdom election resulted in a hung Parliament, meaning the May's Tory Party needed to do a deal to beef up its numbers if key Commons Votes.
■ An extra £1billion in funding will go to Northern Ireland, mainly over the next two years, with £400m earmarked for infrastructure projects, £200m for improvement of the health service and the rest going on ultra-fast broadband, tackling deprivation, health and education pressures and mental health services.
Discussions on a deal between the Conservatives and the DUP began immediately after the election, stirring up further resentment against the embattled May who was left weakened by the political setback.
Both parties had agreed there will be no change to the pensions triple lock and the universal nature of the winter fuel payment across the United Kingdom, things May had planned to change in her election manifesto but later dropped.