The Lakers announced the deal Wednesday.
Harris spent the past four years at Gonzaga, averaging 14.6 points and 7.4 rebounds last season while earning all-conference honors for the second time.
After going undrafted, Harris was a versatile contributor for the Lakers during summer league play in Las Vegas last month. He averaged 10.2 points and 5.6 rebounds while starting five games.
The 6-foot-8 Harris is from Speyer, a city in southwest Germany. He played for the German national team in the 2010 world championships and the 2009 European championships.
Lakers center Chris Kaman also has played for the German national team.