England goalkeeper Fraser Forster does not know if he will still be at Celtic when they next play in Europe.
Norwich captain Sebastien Bassong has signed a new two-and-a-half-year contract.
Cooper spent six years at the helm of the Highland club between 1996 and 2002.
The ex-Aberdeen and Rangers player was most recently in charge at Hartlepool United, where he had a couple of spells as manager.
Adams was pleased to see Cooper back at the Dingwall outfit as part of a restructuring of the backroom team.
He told the club's website: "We've got an extremely small staff here at Ross County and it is vital that we have a structure in place and have the right people in place to take the players, team and indeed the club forward.
"Neale is someone that I've known for a number of years and having had him join us for a couple of days of training it was obvious his qualities complemented what we already had in place here, so I'm delighted that he's agreed to join us."
Cooper will be in the dugout for Saturday's match against Dundee United.
The visit of the Tayside club is the first of two back-to-back home fixtures for County, with St Mirren making the trip north midweek, and Adams is keen to make home advantage count.
He said: "We've been on our travels for eight out of 14 games in the SPL and we've got two home games now.
"Dundee United are a very good side. I watched them against Kilmarnock and they have excellent attacking players. We're in for an exciting match.
"The players here enjoy playing in the big occasions and we've done exceptionally well against Aberdeen and Hibs in the recent home games.
"United are a team who can cause any team problems on their day. They did well against Celtic recently as well.
"We're just looking to put the onus on Dundee United and hopefully we can come away with a win."