BANGKOK, June 24 (Reuters) - Thailand's newly elected lawmakers will meet for the first time in a parliamentary session on July 3, a royal decree published on the official royal gazette website said on Saturday.

The decree sets a motion for the formation of a new government, following the general election in May, with the vote to elect a new prime minister likely to be held in July.

The country's election commission on Monday certified the winners of all 500 seats of the lower house which must convene within early July to elect a speaker and two deputies. The speaker will then call for a joint session of parliament between the elected lower house and the appointed senate to vote on a new prime minister.

The progressive Move Forward party pulled off a stunning victory in the May 14 ballot, closely followed by the populist Pheu Thai party, thrashing conservative rivals allied with the royalist military after nine years of government led or backed by the army.

An eight-party alliance made up of the opposition is expected to back Move Forward's Harvard-educated leader Pita Limjaroenrat for prime minister and form a coalition government, likely within the next month.

The alliance has control of 321 seats, still short of the 376 needed in the vote for the next premier. To elect Pita prime minister the alliance will have to must a majority of the 500 seats in the lower house and the 250 seats in the senate. The senators were appointed under military rule after a 2014 coup.

The Move Forward Party won the election on an anti-establishment platform that has put it on a collision course with conservatives royalist generals and old-money business elite that have long controlled Thai politics.