The 21-year-old Scotland international is available to make his Seagulls debut in Sunday's home Premier League clash with Leicester after joining from Chelsea on a four-year deal on deadline day.
The midfielder made 11 Premier League appearances for the Blues before getting more top-flight experience during a season-long loan spell with Norwich last term.
Gilmour has yet to play any competitive football so far in the 2022-23 campaign, so may have to wait until he has built up sharpness before making his first Brighton appearance.
But Potter is confident Gilmour will impress during his time at the Amex Stadium, pointing to his technical ability as an asset.
The Seagulls boss told a press conference, quoted on the club's Twitter account: "Billy's an exciting signing for us, he's an able footballer and a great character, he has a great personality.
"He'll fit into the group and add competition in midfield. We're really pleased to have him here.
"As a footballer, Billy's very technically able. He benefits from structure and the team functioning well, which is our job.
"If we do that, I think he will have a really good time here."
Fourth-placed Brighton head into Sunday's contest looking to bounce back from their first defeat of the season at Fulham in midweek.
Their opponents Leicester sit bottom of the table, having managed just one point from their opening five games.