The Whites defender is looking forward to lining up with the midfielder again this season.
Bridcutt impressed during a seven-month loan spell at Elland Road last season and was a key man for former manager Steve Evans.
After weeks of speculation and negotiation, Evans' successor Garry Monk completed a deal earlier this month for the 27-year-old to return to Yorkshire on a permanent deal.
That move was generally seen as a wise one, with Bridcutt's experience and physicality a big plus point for the Whites in midfield last term.
Speaking to BBC Radio Leeds after the 1-1 draw with Fulham on Tuesday night, Cooper admitted that he was glad to see the former Sunderland midfielder brought back to the club.
Cooper said: "[He brings] a lot of experience. He's played in the Premier League and I think the manager has clearly said that he is only going to putting in players who are going to better us, and I think Liam does, definitely.
"He’s a good player, we've all seen what he is about last year. He can get stuck in, he will give his all, and that’s all you can ask for."
Bridcutt did not feature in the matchday squad for the clash at Elland Road, but he will be looking to get up to speed and cement a place in Monk's starting XI as soon as possible.
He will be aiming to force his way into contention for the Yorkshire derby with Sheffield Wednesday on Saturday lunchtime.