Former Turnbull government minister Scott Ryan has been elected Senate president, replacing Stephen Parry who was ensnared in the citizenship saga.

Senator Ryan resigned from his role as Special Minister of State to replace Mr Parry who left parliament after it was revealed he held dual citizenship.

The Victorian Liberal senator defeated Greens candidate Peter Whish-Wilson in a ballot on Monday.

"It was not a circumstance I thought would present itself nor one I thought would present itself to me in the year immediately," Senator Ryan told parliament.

The Greens argued a crossbench president would restore integrity to parliament.

"This government and the way it has handled this citizenship crisis, is a disgrace, and you have brought disrespect onto the position of the president of the Senate by how you have handled this constitutional crisis," Senator Whish-Wilson said.

Senator Ryan picked up 53 votes, ahead of Senator Whish-Wilson with 11, while there was one invalid ballot paper.