On January 8, 2016, Morris was awarded the Hermann Trophy as the best player in NCAA Division I soccer.
After winning the NCAA Division I Men's Soccer Championship, there was speculation that Morris would begin to play professionally. Coach Jürgen Klinsmann stated that Morris "obviously has to" turn pro. On January 5, 2016, Morris announced he decided to forgo his senior season at Stanford to turn pro. It was widely speculated that Morris would sign with the Sounders, the club for which his father works, and also holds his amateur rights. On January 21, 2016, Morris signed with Seattle Sounders FC, being given MLS's highest-ever Homegrown Player contract worth roughly $250,000 a year. He joined the Sounders' preseason training camp in Arizona, debuting in a friendly against Celaya F.C. on February 9, 2016. On February 23, 2016, Morris made his professional debut against Club América in the CONCACAF Champions League, starting the match. The following week, he debuted in the Sounders' first Major League Soccer game of the season against Sporting Kansas City.
Morris scored his first Major League Soccer goal for the Sounders on April 16, 2016, against the Philadelphia Union. He then went on to score in his next three consecutive games, matching the Seattle rookie scoring record, his next goal then surpassed the rookie goalscoring record which had been set by Steve Zakuani in 2009. He has since helped his team to win the MLS Cup after a run from ninth place into fourth, along with the help of Nicolas Lodeiro, a new midseason acquisition made by Seattle.
On January 5, 2016, it was reported that Morris was set to train with Werder Bremen at their winter camp, which Bremen chief executive Thomas Eichin claimed was "an opportunity for us to get to know the player better. Nothing more and nothing less". On January 13, 2016, it was reported that Bremen extended the trial of Morris who then played in a friendly match against Inter Baku PIK and recorded an assist. On January 18, 2016, it was reported that Bremen had offered a contract to Morris, and Eichin claimed he was confident that they would sign him. However, it was later reported by Werder Bremen that Morris had turned down their offer in favor of playing in the United States.