Booth has spent the past two seasons in the KHL, most recently with Avangard Omsk.
He put up four goals and nine assists in 19 games with Omsk last season, and came to Red Wings camp on a professional tryout agreement.
The Athletic’s Craig Custance is reporting that the deal carries a $700,000 NHL salary, and a $250,000 AHL salary.
The 32-year-old last played in the NHL in 2014-15 with the Toronto Maple Leafs, scoring seven goals and 13 points in 59 games.
The Detroit native is a one-time 30-goal scorer, having reached the mark in a career-best 60-point season with the Florida Panthers in 2008-09.