The British government has agreed to introduce an Irish language act in Northern Ireland if Stormont fails to do so by the end of September.
Speaking in the early hours of Thursday, Sinn Fein leader Mary Lou McDonald said: “Irish speakers have been waiting for 15 years for basic rights and recognition to be delivered.
“This is important for Irish language speakers and for wider society because power sharing is based on inclusion, respect and equality.
“There is an important responsibility on the Irish and British government to ensure no further delay.”
Arguments over the promised legislation had threatened to prevent attempts to resume business at Stormont.
Sinn Fein had asked the British government to go over the heads of the assembly, saying it would not return to power-sharing with the DUP without a firm commitment on the legislation.
The DUP had indicated it would not commit to a definite timetable.
Ms McDonald said: “We told the British government that this is the only viable option to deliver these rights as the DUP were unwilling and incapable of delivering on their commitments.
“It is deeply regrettable that the DUP chose to block rights in this way for so long.
“Tonight we have broken through all of that.”
As a result, Northern Ireland Secretary Brandon Lewis said the DUP and Sinn Fein had agreed to nominate first and deputy first ministers “at the earliest opportunity”.
He said he was “disappointed” the Irish language legislation had not already been brought forward in the Assembly, saying it “rightly reflected the need to respect the freedom of everyone in Northern Ireland to affirm and express their national and cultural identity”.
DUP leader Edwin Poots, who recently succeeded Arlene Foster, is seeking to nominate his conservative colleague Paul Givan to take over as first minister.
Sinn Fein will nominate Michelle O’Neill as deputy first minister.