In a statement, Leadsom said: "The government has agreed with Buckingham Palace that the State Opening of Parliament will take place on 21 June 2017".
In a highly unusual move, Theresa May was forced to push back the speech to Wednesday 21 June amid Tory disarray as they entered talks with Northern Ireland's DUP to gain their support for a minority Government.
Foster had previously said an alliance between the DUP and Conservative Party would help defend Northern Ireland's position as the United Kingdom prepares to begin Brexit negotiations, which are due to kick off next week.
As discussions between the DUP and Tories continued yesterday, a senior Conservative source confirmed there was no requirement for a so-called "confidence and supply" arrangement to be in place beforehand.
Different DUP sources say different things about the approach to Brexit.
The Conservative source said both parties were "committed to strengthening the union, combating terrorism, delivering Brexit and delivering prosperity across the whole country", and that Northern Ireland would get a funding boost.
The leader of the DUP in Northern Ireland, Arlene Foster, has flown home.
This was the case in 2001, when a ten-minute speech was delivered to parliament before the Queen exited, changed from her ceremonial robes into her racing outfit and was taken under a police escort to Windsor Castle.
The State Opening was initially scheduled for June 19 - the same date when Brexit negotiations were due to begin in Brussels.
Any plans that require new legislation are vulnerable to a rebellion of as few as seven Tory backbenchers, even if the prime minister secures the support of the Democratic Unionist Party.
The 1998 Good Friday Agreement, also referred to as the Belfast Agreement, commits the United Kingdom and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
The power-sharing agreement between the DUP and Sinn Fein broke down late past year.
In a letter to Mr Davis, they said it was vital agreement was reached on how the devolved administrations would be represented at the talks.