Gasol has averaged 18.3 points and 9.2 rebounds while connecting on 51 percent of his shots in his NBA career for the Lakers and Memphis.
His arrival helps boost the chances of the Bulls to become a title contender despite the nagging injury problems that have hampered playmaker Derrick Rose the past several seasons.
"It hasn't been easy," Gasol tweeted. "After meditating it a lot I've chosen to play with the Chicago Bulls. Looking forward to this new chapter of my career."
Gasol also was courted by the reigning NBA champion San Antonio Spurs.
The Bulls might have to make other moves before signing Gasol due to NBA salary cap restrictions.
No word was indicated on how long or rich a deal Gasol might have.
But his signing does appear to drive the final nail in any notion that New York Knicks star Carmelo Anthony might sign with the Bulls rather than remain in New York with a team that failed to make the playoffs last season.
Gasol helped Spain capture the silver medal at the 2008 and 2012 Olympics, both times falling to the US collection of NBA stars in the final.