McGuinness told Irish radio last year's deal between Irish nationalist Sinn Fein and Paisley's pro-British Democratic Unionist Party had been "one of the most historic political breakthroughs in the history of the island of Ireland."
He and Paisley have been dubbed the "chuckle brothers" after a string of unexpectedly jovial and friendly joint appearances over the last year that are seen as one of the most potent indications of how much things have changed.
Paisley himself was once best known as a burly, bull-necked preacher with the loudest voice in Northern Ireland who would bellow "No Surrender to Dublin" from pulpit and husting.
Sinn Fein President Gerry Adams said there was no reason anybody should be concerned by Paisley's departure.
"He (Paisley) had a certain personality and whoever is the new leader will bring their own personality and characteristics to bear," Adams told Reuters.
Paisley's son, Ian Paisley Jr, resigned as a junior minister in the Northern Ireland power-sharing government last month, bowing to criticism of his links to a property developer.
Paisley said he was not stepping down because of his son's tribulations. "That had no effect on me whatsoever ... In fact, it hardened me to realise there was no easy path and we had to prepare for the rough and the smooth," he told BBC television.
Prime Minister Gordon brown said Paisley had made a "huge contribution" to political life in Northern Ireland.
"The whole country values and admires the manner in which he has led as First Minister," Brown said.
Paisley's deputy Peter Robinson is odds-on favourite with bookmakers to take over as head of the DUP but Paisley refused to be drawn over his successor.
"The DUP is not the Roman Catholic church. We don't have apostolic devolution. It comes by the votes of the people."
