Adams, who resigned from his post at League One side Port Vale last month, takes over at Prenton Park with the Birkenhead club bottom of English football's fourth tier with just nine points from 12 games.
The appointment comes only three days after Rob Edwards was sacked and 52-year-old Adams is determined to pull Tranmere away from the relegation zone.
"I'm delighted to be given the opportunity to manage Tranmere Rovers by the chairman and board of directors," Adams told the club's official website.
"The immediate task is to get the club off the foot of the table. There's a lot of hard work ahead but it's a challenge I'm relishing.
"Tranmere is a good club with a proud history and one which shouldn't be near the bottom of the division. In the weeks and months ahead I'll be doing everything I can to drive the club forward and to a much healthier position."
Adams will not be in dugout for Saturday's visit to Oxford United and will instead take charge for the first time against Mansfield Town next Tuesday.
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