The Grange will host both matches on 15 and 17 June.
The nations met at the World Twenty20 in 2016, with the Scots all out for 136 in the final over of an 11-run defeat in India.
"This will be the first full member ODI that I have been involved in outside of a World Cup," said Scotland head coach Grant Bradburn.
"The players will be desperate to match their skills against Zimbabwe on home soil."
Zimbabwe are 11th in the International Cricket Council's (ICC) ODI rankings, the lowest-ranked of the 10 Test-playing sides.
They lost a home ODI series 3-2 to ICC associate members Afghanistan - who are above them at 10th place in the rankings - in February.
Scotland meet Namibia in the Intercontinental Cup at Ayr (6-9 June) and play two 50-over World Cricket League Championship games against the same opponents at The Grange on 11 and 13 June.
After four matches, the Scots are sixth in the Intercontinental Cup standings, one place above Namibia.
Before those games in June, Bradburn's side will face Sri Lanka in two 50-over matches in Kent on 21 and 23 May as their opponents warm up for the ICC Champions Trophy - although they will not be classed as official ODIs.
Scotland will play two one-day internationals against Zimbabwe in Edinburgh this summer.