The Foyle MP said that there should be no impediment to the quick restoration of the Assembly and Executive to get on with the business that politicians were elected to undertake.
Mr Eastwood warned other political leaders that there should never again be a move to tear down the institutions of the Good Friday Agreement for party political advantage.
Said Mr Eastwood: “This news has been a very long time coming.
“Years of stagnation have led to serious damage to public services, the position of public sector workers, the health of people waiting unreasonable times for hospital treatment and, ultimately, to public confidence in the political process.
“In spite of that, this is a better day for people across Northern Ireland and I am optimistic that the democratic institutions can be restored in short order.
“The optimism of this moment, however, will be tempered by the performance of a new Executive which has an enormous in-tray.
“The SDLP’s priorities for a long time now have been to restore the government, rescue public services and reward workers with a fair pay award.
“Those are the urgent challenges facing incoming Ministers and our team will hold them to it.
“We will hold conversations with the British and Irish Governments today and tomorrow about the shape of the legislation to be tabled at Westminster, the prompt restoration of the North-South institutions and our proposals to make sure that no party can ever put us in this position again.
“There is no time to waste now.
“The deal has been done.
“Let’s get to work,” added Mr Eastwood.