Mr Stoddard will also relinquish his role as a director on the firm’s board from 30 June.
Aviva says Mr Stoddard will remain with the group until 31 December “to support an orderly transition”.
Jason Windsor, currently chief financial officer of Aviva UK Insurance, will become interim CFO on 1 July.
He joined Aviva in 2010 and was said to have “extensive experience of the group, including as chief capital and investments officer, and as a member of the group executive”.
His appointment is subject to regulatory approval.
Maurice Tulloch, Aviva chief executive, said: “Tom is a tremendous leader and has played a major role in delivering Aviva's financial turnaround, significantly strengthening the group's capital position.
“After five successful years at Aviva, he leaves with my best wishes and those of Aviva's Board.”
Mr Stoddard said: “Whilst I will miss all the friends I have made here, Aviva has a strong finance team, and it is now time for me to clear the way for others to step up, as I consider new opportunities.
“Aviva is in a strong financial position with a bright future ahead of it.
“I have thoroughly enjoyed working with Maurice and I wish him, Jason, and everyone who works for Aviva all the best for the future.”