The Scottish Rugby Union's decision last week to order Edinburgh to leave the national stadium means Stewart's Melville's home ground will stage their first match of the summer.
The SRU announced that Edinburgh had terminated their operating agreement with the union, making them ineligible to play at Murrayfield.
Edinburgh coach Lynn Howells said: "With an influx of up to 15 new players to Edinburgh over the summer, this is an ideal opportunity for our supporters to see what the squad promises for the coming season.
"As they always do, the Tongans will provide a physical challenge and with the stage they are at in their World Cup preparations they will be looking to implement their game plan. It is certainly an exciting fixture to start our season."