[9] His cousin, Erskine Kelley, played minor league baseball with the Pittsburgh Pirates and Chicago Cubs organizations.

[20] After starting his professional career with the Low-A Vancouver Canadians, the Blue Jays promoted Stroman to the Double-A New Hampshire Fisher Cats on August 1, 2012.

[21] Stroman was suspended for 50 games on August 28, 2012, for testing positive for methylhexanamine, a banned stimulant, which he claimed to unknowingly consume in an over the counter supplement.

[32] Stroman was optioned back to Triple-A Buffalo on May 18, and was recalled on May 30 to make his first Major League start the following day.

[39] Stroman pitched four innings in relief of Drew Hutchison's final start of the season on September 26, and earned his first career save.

He did not appear in the final two games of the Blue Jays season, and finished 2014 with an 11–6 record, 3.65 ERA, 111 strikeouts, and a 1.17 WHIP in 1302⁄3 innings pitched.

[44] While rehabbing from the injury, Stroman returned to Duke University to finish his degree, majoring in sociology with a minor in Markets and Management Studies.

[50] On September 2, he made his Class-A debut with the Lansing Lugnuts and pitched 42⁄3 innings, yielding no hits while walking one and striking out seven.

Stroman pitched five innings and earned the win, yielding three runs before being removed due to a rain delay.

[56] He started again in Game 5 of the same series, allowing six hits and two earned runs over six innings in an eventual 6–3 Blue Jays victory.

[58] He pitched into the ninth inning, holding the Tampa Bay Rays to three runs on six hits, while striking out 5 in a 5–3 win.

[60] Stroman improved on his single-game strikeout record on August 1, when he struck out 13 Houston Astros batters in a no-decision.

[62][63] On October 3, the Blue Jays announced that Stroman would start the Wild Card game against the Baltimore Orioles the following day.

[65] Stroman was scheduled to start the fourth game of the ALDS against the Rangers, however the Blue Jays swept Texas and advanced to play the Cleveland Indians in the American League Championship Series.

[67] Stroman hit an opposite field home run off Julio Teherán in the Blue Jays 9–0 win over the Atlanta Braves on May 18, 2017.

In doing so, Stroman became just the second Blue Jays pitcher to hit a home run, joining Mark Hendrickson, who did so on June 21, 2003.

[69] He also became the first pitcher listed 5 feet 8 inches (1.73 m) or shorter to hit a home run in the majors since Tom Phoebus of the Baltimore Orioles did so in 1968.

[70] On July 3, Stroman left a game against the New York Yankees after five innings when a blister developed on his right middle finger, though the injury did not cause him to miss a start.

[71] Stroman was hit on the right elbow by a line drive in Toronto's 7–2 win over the Baltimore Orioles on September 2, and was forced to leave the game,[72] though he was once again able to make his next start.

[75][76] On October 28, Stroman was named a finalist for the American League pitcher's Gold Glove Award, along with Alex Cobb and Chris Sale.

[78] The Toronto chapter of the Baseball Writers' Association of America unanimously voted Stroman the Blue Jays' Pitcher of the Year for 2017.

[81] On June 13, he made his High-A debut with the Dunedin Blue Jays and pitched 41⁄3 innings in a rehab start, surrendering two runs on one hit while walking four and striking out three.

[83] Later in the season, Stroman was forced to leave starts on August 7 and 17 against the Boston Red Sox and New York Yankees, respectively due to blisters in his pitching hand.

[86] On March 13, 2019, Stroman was announced as the Opening Day starter by Blue Jays manager Charlie Montoyo.

[88] On July 28, 2019, the Toronto Blue Jays traded Stroman (along with cash considerations) to the New York Mets for pitching prospects Anthony Kay and Simeon Woods Richardson.

On December 1, 2021, Stroman signed a two-year contract (with a player option for a third year) worth $71 million to play for the Chicago Cubs.

[114] His other tattoos include the area code 631, portraits of his parents, a Gold Glove Award, the Air Jordan logo, a quote from Mark 9, a quote from Martin Luther King Jr., the flag of Puerto Rico, his mother's eye, the Major League Baseball logo with the date of his MLB debut, the date of his 2015 knee surgery, a portrait of Rihanna, Cillian Murphy's character from Peaky Blinders, Denzel Washington's character from Training Day, himself swinging a bat in a Blue Jays uniform, the skyline of Toronto, the head of a lion, his father's police badge, his own initials, an orchid, a poker chip, the number 6, a silhouetted airplane, and a wine glass as well as "God bless me," "God save me" and "family" in Spanish and the words "blessed," "mamma's boy," "daddy's gift," "dreamchaser," "BElieve in YOUrself," "smile," "mom," "dad," "height doesn't measure heart" and "breaking stereotypes.

"[115][116] On January 9, 2015, Stroman completed the legal process for trademarking "Height Doesn't Measure Heart" and "HDMH".

[118] He has also partnered with Nike, Jordan Brand, BioSteel, and Rogers to create apparel featuring the HDMH logo.