Glendening has been a valuable member of the Red Wings' checking line this season, contributing six assists in 51 games in his first NHL season.
"Glendening definitely earned himself a contract," coach Mike Babcock said. "Now he's set up to be a Red Wing."
The 24-year-old native of Grand Rapids, Mich., played four seasons at the University of Michigan before signing as an undrafted free agent with the Boston Bruins. He played in three games for their American Hockey League affiliate in Providence at the end of the 2011-12 season and in 51 games for the Grand Rapids Griffins last season, scoring eight goals and 26 points.