[1][2] The San Francisco Giants selected Webb in the fourth round of the 2014 Major League Baseball draft.

[6] In 2018, Webb pitched for the San Jose Giants and Richmond Flying Squirrels,[8][9] posting a combined 2–5 record with a 2.41 ERA in 27 games (26 starts).

He added, "I know in my heart that something someday will be put into the world to prove my innocence" and "I love this game and respect it too much to ever cheat it".

He then apologized for bringing "negative attention" to his "family, friends, teammates, & the San Francisco Giants" and promised to "be back better than ever" after his suspension.

[16] He made his major-league debut that night versus the Arizona Diamondbacks, allowing one run while striking out seven batters over five innings.

[20] Webb was the starting pitcher in the last game of the season, with the Giants having a one-game lead in the National League West over the Los Angeles Dodgers.

In Game 5, he joined Bumgarner, Christy Mathewson, Ryan Vogelsong, and Jack Sanford as the only pitchers in franchise history with multiple appearances of seven innings and one earned run or fewer in a single playoff series.

[19] Webb was the first Giants pitcher to win 15 or more games in a regular season since Madison Bumgarner and Johnny Cueto both accomplished the feat in 2016.

[25] On January 13, 2023, Webb agreed to a one-year, $4.6 million contract with the Giants for the 2023 season, avoiding salary arbitration.

[19] Webb was named an NL Cy Young Award finalist for 2023 and finished second in the voting to San Diego's Blake Snell.

Webb cited a desire to play with the Giants for the duration of their spring training camp as a motivation for his decision to opt out.

[36] Webb releases the ball from a low arm slot that maximizes the unique movement of his pitches.

[38] Webb is considered legally blind and was diagnosed with severe astigmatism in third or fourth grade when he had difficulty seeing the ball.