He tallied eight goals and six assists in 18 games with LAFC in 2020 and was named the MLS Comeback Player of the Year.
The 35-year-old forward led the Major League Soccer with 27 goals in 2014 and with 24 goals in 2016, both while with the New York Red Bulls. He ranks sixth in MLS history with 116 goals in 213 matches with NYRB (2013-19) and LAFC.
"We are thrilled that Bradley has chosen to join Crew SC as we look to build off of our 2020 MLS Cup title and continue to contend for trophies headed into 2021," Crew president and general manager Tim Bezbatchenko said in a team release. "As one of the most proficient strikers in our league over the last decade, Bradley brings valuable veteran experience to our attacking corps and we look forward to his contributions.
"We also believe Bradley's quality character and mentality is an asset to every team he has played for and has played a critical role in all the personal success he's had in his career."
Wright-Phillips is a two-time MLS Best XI selection (2014, 2016) and a three-time MLS Supporters' Shield winner (2013, 2015, 2018).
Also on Wednesday, the Crew saw backup goalkeeper Andrew Tarbell sign with expansion side Austin FC. He made several appearances this season for Columbus after joining from San Jose.