Foster, whose party has been losing support in the region, will leave as party leader on May 28 and then as FM at the end of June.
The senior politician was facing rising anger over her party’s handling of Brexit and its decision to abstain in a vote on gay conversion therapy.
Earlier this week, it emerged a letter of no confidence in her leadership had been circulated among DUP MPs and MLAs (members of the legislative assembly in Northern Ireland).
In a statement on Wednesday, Foster said she intended to “depart the political stage” and that her decision would spark a contest for her replacement.
“It has been the privilege of my life to serve the people of Northern Ireland as their first minister and to represent my home constituency of Fermanagh/South Tyrone,” she said.
“I first entered the assembly in 2003 and undoubtedly the journey of the last 18 years has been memorable. There are many people who have helped and supported me throughout that period and I will always be grateful for the kindness and support shown to me by them.
“Whilst there have been many difficult and testing times for the executive it remains my firm view that Northern Ireland has been better served having local ministers at this time.
“It is unthinkable that we could have faced into the coronavirus pandemic without our own devolved ministers in place and no ministerial direction for departments.”
There has been growing unease among DUP members about Foster and the wider party leadership in recent months.
The primary source of concern is the handling of the Brexit process. The DUP is facing anger from the wider loyalist and unionist community for the introduction of an Irish Sea border.
Critics have accused Foster of failing to use the party’s influence at Westminster – particularly during its confidence and supply deal with the Conservatives – to secure a Brexit deal that saw Northern Ireland leave the EU on the same terms as the rest of the UK.
She has also been accused of not being vociferous enough in opposition to the contentious protocol, which governs the new Brexit trading barriers between NI and GB, ahead of its introduction at the start of 2021.
Poor recent polling numbers have exacerbated the discontent within the party faithful, who are mindful of next May’s looming Assembly election.
Foster added: “It is important to give space over the next few weeks for the party officers to make arrangements for the election of a new leader. When [they are] elected, I will work with the new leader on transition arrangements.”
Agriculture minister Edwin Poots, who is viewed as a more hardline figure, is among those thought to be preparing a bid for the DUP leadership.