Norris, 31, has a wealth of experience having made over 400 career appearances for the likes of Bolton, Hull, Plymouth and Ipswich.
He joins former Pompey team-mates Jason Pearce, Jamie Ashdown and Luke Varney in moving to Elland Road this summer.
Warnock told the Whites' official website: "He has good energy and the way we are at the moment, you can't get enough good players in that area.
"I think he'll fit in well, he'll fight for his place and give us the competition."
With Snodgrass having left Leeds' training camp ahead of a possible move to Norwich, Warnock added: "I'm looking for goals from midfield to help us with the loss of Snodgrass. We need to compensate that even though we're looking to sign strikers."