The Prime Minister has said Martin McGuinness moved the republican movement towards peace.
Theresa May recognised his work in securing a number of significant political agreements.
Sinn Fein president Gerry Adams hailed him as a patriot and peacemaker as tributes flooded in from across the political spectrum.
The Prime Minister said: “He played a key role in moving the republican movement towards a position of using peaceful and democratic means.
“I want to send him best wishes for his retirement.
“We will all continue to work to make sure that the people of Northern Ireland are able to live freely and in peace.”
The Sinn Fein president said they first met more than 45 years ago behind the barricades of Free Derry, a no-go zone for the British army, and had been friends and comrades since.
“I also want to thank Bernie (his wife) and the entire McGuinness family for the support they have given to Martin over many years and for allowing him to become the leader, the patriot, the peacemaker and poet that he is.”
He said he had been shocked by Mr McGuinness’ recent appearance.
“Thank God he is looking a lot better since then and responding well to the treatment he is receiving. However, he does need to take time out to get better for himself, for his family and for our struggle.”
He added: “Martin has said he wants to come back and be part of the process to end partition, build reconciliation, unite our people and achieve Irish unity.
“Give him the space to get better and increase our efforts so that when he returns the process of change has advanced.”
Northern Ireland Secretary James Brokenshire said he was sorry the former deputy first minister would not be standing for another term at the Assembly.
He said: “I thank him on behalf of the Government for his work in securing a number of significant political agreements as well as his service as deputy first minister of Northern Ireland.”
Picture: Prime Minister Theresa May (centre) with former First Minister Arlene Foster (left) and former Deputy First Minister Martin McGuinness at Stormont Castle in Belfast. (Charles McQuillan/PA).