UK Prime Minister Mr Johnson said he hoped Mrs Foster will continue in public service after she bowed to a major internal heave against her.
The 50-year-old Fermanagh and South Tyrone Assembly Member suggested an intent to quit politics altogether, with her resignation statement speaking of preparing to “depart the political stage”.
Mr Johnson tweeted: “I want to thank Arlene Foster @DUPleader for her dedication to the people of Northern Ireland over many years.
“She will continue to play a vital role as First Minister until June and I hope that she stays in public service for years to come.”
Secretary of State for Northern Ireland Brandon Lewis described Mrs Foster as a “truly dedicated public servant” who had devoted her political career to the people of Northern Ireland.
He said there would be many young people who will be inspired to follow her path into political life and he wished her all the best.
Mr Lewis tweeted: “Arlene is a truly dedicated public servant, devoting her political career to her constituents for over 18 years and the people of NI as FM for several years.
“There are many young people, particularly young women, who will be inspired by her example to follow a path into politics.
“I wish her all the best and look forward to continuing to work with her in the days and weeks ahead, delivering for all the people of NI.”
Mrs Foster’s handling of Brexit and in particular the Northern Ireland Protocol has created growing unease among DUP members in recent months.
The DUP is facing anger from the wider loyalist and unionist community for the introduction of an Irish Sea border.
Critics have accused Mrs 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.