Financial terms were not disclosed, but the Nuggets said they signed Young to the injury-hardship relief exception, which is granted by the NBA, and waived guard Brandon Goodwin in a corresponding move.
Denver guards Will Barton (groin) and Gary Harris (hip) and forward Paul Millsap (toe) are sidelined with long-term injuries.
Millsap broke a toe on his right foot in last Friday's game against Charlotte, ESPN's Adrian Wojnarowski reported last week. The injury is expected to sideline Millsap 4-6 weeks, Yahoo reported Monday.
Young, 33, played 80 games last season with the champion Golden State Warriors but remained unsigned since becoming a free agent.
The 6-foot-7 Young should provide some much-needed depth for the Nuggets, who went into Monday night's game against the Memphis Grizzlies with a 17-9 record.
Young has averaged 11.4 points per game over parts of 11 seasons with five different teams.