The versatile defender has found first-team opportunities hard to come by this campaign, with his only appearance for the Hammers coming in the Capital One Cup victory over Burnley.
Potts told Pompey's official website: "I was told about Pompey's interest yesterday, so I grabbed my gear and came straight down here.
"Despite the division they now find themselves in, they are still regarded as a massive club.
"The thought of playing at Fratton Park in front of the sort of crowds that come to Pompey is a really exciting prospect.
"I just want to play first-team football, so hopefully I can benefit the team and help us get some good results."