Central defender Vitorino Hilton has signed a one-year contract extension with Montpellier.
AC Milan have completed the permanent signing of defender Cristian Zapata from Villarreal for an undisclosed fee.
Archibald has been in interim charge since Jackie McNamara and assistant Simon Donnelly left Firhill to take over at Dundee United in late January.
The Thistle defender has helped maintain their promotion push, with the Jags two points behind Irn-Bru First Division leaders Morton with two games in hand.
Chairman David Beattie said: "I'm absolutely delighted to be able to confirm the appointment of Alan Archibald as Partick Thistle manager and Scott Paterson as his assistant.
"I look forward to working closely with them as we continue to work hard at providing a club that we can all take pride in."