As he entered Downing Street, Scottish Secretary David Mundell said he was “very positive” about Mrs May taking over from Mr Cameron.
He said: “She’ll be a great prime minister for this country and someone who can unify the country and get on with the big job of negotiating Brexit.”
Mr Mundell said he expected “very many kind words” for Mr Cameron, adding: “David Cameron has done an incredible job in turning the Conservative Party round.
“If you look where we were in 2005 people even then said there would never be another Conservative Government.
“In 2010 he became the Prime Minister and took on that very difficult job of turning around the economy and dealing with the Coalition arrangements which were a challenge.
“In 2015, a majority Conservative Government. So David Cameron’s record as Conservative leader is a very proud and strong one.
“Of course there’ll be sadness but we’re in a position of change and that’s the nature of politics, that’s the nature of our democracy.
“So I will be sad for David, Samantha and his family that they are moving on but I think he will be able to be very proud of his record as Prime Minister and they way that he has served our party and our country.”