The Liberal Democrat leader has praised Mr Cameron for forming a coalition government but said his main political legacy would be taking the UK out of Europe to the "huge detriment of future generations".
Tim Farron said that the former prime minister had "demonstrated a capacity to think above and beyond tribal politics" by creating the first post-war coalition government between 2010 and 2015.
He also praised Mr Cameron's qualities of "personal courtesy, humour and thoughtfulness" but said the former leader would be mainly remembered for taking the UK out of the EU in a damaging "gamble".
He has lots of things that he should be proud of but sadly his legacy will be one of accidentally removing us from our closest friends and neighbours in Europe.
He took a politically motivated and short-termist gamble with our country's future, and lost to the huge detriment of future generations. He now leaves the rest of us to pick up the pieces.
Theresa May has said she was "proud " to work in David Cameron's government as she thanked him for his service to the country.
The new prime minister said that the Conservatives had achieved "great things" under her predecessor as he resigned from parliament.
I was proud to serve in David Cameron’s Government – and under his leadership we achieved great things. Not just stabilising the economy, but also making great strides in delivering serious social reform.
His commitment to lead a one nation Government is one that I will continue – and I thank him for everything he has done for the Conservative party and the country.
I wish him and his family well for the future.
Former Conservative leader William Hague has praised David Cameron for his decision to stand down as an MP.
Mr Cameron has said that he did not want to become a "distraction" from the work of Theresa May's government.
Mr Hague agreed, saying former prime ministers were either viewed as a diversion or accused of doing too little.
Right decision by David Cameron to leave Commons - former Prime Ministers are either accused of doing too little or being a distraction.
David Cameron has told ITV News he has no plans for the future after resigning as an MP.
ITV News Deputy Political Editor Chris Ship tweets:
David Cameron told Theresa May of his decision to stand down as a Tory MP this afternoon
David Cameron says he has no current plans for his future but, as former Prime Minister, can't be full constituency MP for people of Witney
The former prime minister has stepped down from his position in parliament as he resigned his seat as the MP for Witney.Read the full story ›
He rose to lead the country before an equally dramatic downfall after failing to persuade the public to vote to remain in the EU.Read the full story ›
Former Chancellor George Osborne is among the people recognised by the former Prime Minister as he left office.Read the full story ›
David Cameron has been accused of 'cronyism' after a leak of his resignation honours list.Read the full story ›
David Cameron, who resigned as prime minister on Wednesday, has condemned the "sickening and dreadful" attack in Nice.
A sickening and dreadful attack in Nice. I know we stand with the French people and share their values. They shall never defeat us.