Mr Orban is a nationalist politician with close ties to Russia’s President, Vladimir Putin.
He has often blocked EU efforts to send military aid to Ukraine.
Sweden is one of the EU countries which have accused Hungary of backsliding on the EU’s democratic principles.
In turn, Mr Orban’s spokesman, Zoltan Kovacs, accused officials in Sweden of sitting on a “crumbling throne of moral superiority”.
Last week, however, Mr Orban hosted his Swedish counterpart, Ulf Kristersson, and announced his support for Sweden’s membership.
Monday’s vote was almost unanimous – 188 to 6.
In his speech, Mr Orban sharply criticised unnamed Nato allies for exerting pressure on his government to end the 21-month delay.
“Hungary is a sovereign country and does not tolerate being dictated to by others, on the content or timing of decisions,” he said.
The parliament’s approval must now be signed by the president – after which a formal invitation is sent to Sweden to join the 31-member-strong group.
The process usually lasts a few days.
Turkey had been the other Nato country to withhold approval of Sweden’s application in a row over what it called Sweden’s support to Kurdish separatists. It eventually lifted its veto in January.
Every member has a veto over the expansion of the defensive alliance.
Sweden and its eastern neighbour, Finland, both long considered militarily neutral, announced their intention to join Nato in May 2022. —BBC
