Peiris and the other three appointees -- for public administration, urban development and energy -- are all members of Rajapaksa's Sri Lanka Podujana Peramuna (SLPP) party.
The all-important finance ministry post remains vacant at a time when Sri Lanka is in negotiations for a much-needed International Monetary Fund bailout.
Earlier on Saturday, legislators from the SLPP held a closed-door meeting where they resolved to support the new prime minister.
"We have misgivings about Wickremesinghe, but in the national interest to pull the country out of the economic mess, we decided to support the PM," one party lawmaker told AFP.
The main opposition Samagi Jana Balawegaya (SJB) and four other parties have refused to support the government while Rajapaksa remains president.
Huge public demonstrations have for weeks condemned the president over his administration's mismanagement and alleged corruption.
Hundreds remain outside his seafront office in the capital Colombo at a protest camp that has for the past month demanded the leader step down.
Mahinda Rajapaksa, the president's older brother, resigned as prime minister on Monday after his supporters attacked peaceful protesters.
At least nine people were killed and more than 200 injured in ensuing clashes, with dozens of Rajapaksa loyalist homes set on fire by furious mobs.
Mahinda has since been banned by a court from leaving the country and has taken refuge at the Trincomalee naval base in Sri Lanka's east.
Troops have since restored order and a nationwide curfew has been in effect for most of the week.
Wickremesinghe told reporters shortly after assuming office that the country was going through its worst crisis ever.
Sri Lanka has endured months of acute food, fuel and medicine shortages, which Wickremesinghe said would get even worse.