The series begins on August 29, with the second match scheduled two days later, Sri Lanka Cricket said.
The ODIs will be followed by three T20 internationals, the squad for which is yet to be announced.
All five matches will be played in Harare.
Sri Lanka last toured Zimbabwe for a limited-overs series in November 2008.
After Zimbabwe, the Sri Lankan team will take part in the Asia Cup T20 cricket tournament hosted by the United Arab Emirates from September 9.
Sri Lanka squad for two ODIs v Zimbabwe:
Charith Asalanka (captain), Pathum Nissanka, Nishan Madushka, Kusal Mendis, Sadeera Samarawickrama, Nuwanidu Fernando, Kamindu Mendis, Janith Liyanage, Pavan Rathnayake, Dunith Wellalage, Milan Rathnayake, Maheesh Theekshana, Jeffrey Vandersay, Asitha Fernando, Dushmantha Chameera, Dilshan Madushanka.