In an email to staff shared on social media by one of the newspaper's reporters, Lewis said it was "the right time for me to step aside."
A statement from the Post said only that D'Onofrio was succeeding Lewis "effective immediately."
Hundreds of Post journalists -- including most of its overseas, local and sports staff -- were let go in the sweeping cuts announced on Wednesday.
The Post did not disclose the number of jobs being eliminated, but The New York Times reported approximately 300 of its 800 journalists were laid off.
The paper's entire Middle East roster was let go as was its Kyiv-based Ukraine correspondent as the war with Russia grinds on.
Sports, graphics and local news departments were sharply scaled back and the paper's daily podcast, Post Reports, was suspended, local media reported.
Hundreds turned out Thursday at a protest in front of the paper's headquarters in downtown Washington.