It will be her first visit to Washington during Biden's presidency, and likely her final US visit in a long era as chancellor.
Merkel is not seeking a fifth term, and elections to replace her are in September.
She will have worked with four US presidents over her tenure.
The White House said Merkel will visit on 15 July with a long list of issues to discuss with Biden.
The visit comes weeks after Biden decided to waive sanctions on the company behind Russia's Nord Stream 2, an oil pipeline, citing national security reasons.
His top aides suggested he wanted to avoid confrontation with Germany.
Merkel came under intense pressure to back off the project following the poisoning of Alexey Navalny, the Russian opposition leader, but ultimately did not.