The House of Keys seats will be contested in two constituencies within the capital of the island on 21 May.
Bill Henderson and David Cretney, who represented Douglas North and Douglas South respectively, were elected to the Legislative Council last month.
Nomination day - when candidates confirm their intention to stand - will be on 21 April.
The Legislative Council is the upper branch of Tynwald and has 11 members. Four seats became vacant last month.
They did so when the terms of office expired for Phil Braidwood, Dudley Butt, Alex Downie and Alan Crowe.
The Legislative Council primarily acts as a revising chamber for bills, whereas the House of Keys is the directly elected lower branch of Tynwald.
The date of two by-elections has been set following the elevation of two Manx politicians to the Legislative Council.