The Labour leader will sit down with the broadcaster for an hour-long episode of Life Stories – and will also discuss his childhood and career in law.
It will be the first interview with a party leader on Life Stories since former tabloid editor Morgan interviewed Gordon Brown when he was prime minister in 2010.
Sir Keir is expected to discuss his childhood in Surrey, his family life and move into politics from law, culminating in his appointment as Labour leader last April.
The episode is due to be filmed next month and expected to air on ITV in the coming months.
Labour has been in turmoil since the by-election defeat in Hartlepool last week, with setbacks in council elections in England followed by a botched reshuffle.
The results were a major setback for Sir Keir as the party tries to recover from its general election defeat under his predecessor Jeremy Corbyn, which was its worst since 1935.
Morgan said: “It’s very unusual for party political leaders to submit themselves to such lengthy personal interviews and I am delighted that Sir Keir has agreed to talk to me about his fascinating life.
“It promises to be a memorable and very revealing Life Stories show.”
ITV’s head of entertainment, Katie Rawcliffe, said: “Sir Keir Starmer promises to be a real treat for our ITV audience.”
Additional reporting by PA.