Members of the All-Party Parliamentary Group on Iran have been invited by the British/Iran Friendship Group of the Iranian parliament.
Jack Straw, who as Labour foreign secretary led efforts to secure a deal with Tehran over its nuclear ambitions, will be among those travelling next week.
Tory MP Ben Wallace, who chairs the group with Mr Straw, former chancellor Norman Lamont and Labour MP Jeremy Corbyn make up the rest of the party.
A less hardline approach by Tehran to the international community was ushered in earlier this year with the election of Hassan Rouhani as president.
Last month an initial agreement was struck over its atomic ambitions and the UK has begun renewing diplomatic links.
Non-resident charge d'affaires Ajay Sharma then became the first UK diplomat to visit in two years.