Police in Southlake, Texas, said Skaggs was found unresponsive in a room at the local Hilton shortly after 2 p.m. He was pronounced dead at the scene and foul play was not suspected.
The Angels were scheduled to play the first of a four-game series against the Texas Rangers later Monday. That game has been postponed.
"Tyler has, and always will be, an important part of the Angels family," the club said in a brief statement. "Our thoughts and prayers are with his wife Carli and his entire family during this devastating time."
"I am deeply saddened by today's tragedy in Texas," MLB Commissioner Rob Manfred said in a statement. "All of us at Major League Baseball extend our deepest condolences to Tyler's wife Carli, their family, their friends and all of his Angels teammates and colleagues. We will support the Angels organization through this most difficult period, and we will make a variety of resources available to Tyler's teammates and other members of the baseball family."
Skaggs died two days after his last start, in which he lasted 4.1 innings and gave up two earned runs on two hits, walked four and struck out five as the Angels lost 4-0 to the Oakland Athletics. In all, Skaggs made 15 starts in 2019, boasting a record of seven wins and seven losses along with a 4.29 earned run average.
Born in the Los Angeles neighborhood of Woodland Hills, Skaggs was a first-round draft pick of the Angels out of Santa Monica High School in 2009. The Angels traded Skaggs to Arizona in 2010, and he started his big-league career with 13 appearances over two seasons for the Diamondbacks. The Angels reacquired him in December 2013, and he had won 25 games over five seasons with the club.
Skaggs had been a regular in the Angels' starting rotation since late 2016 when he returned from Tommy John surgery. He struggled with injuries repeatedly over the past three seasons but persevered to become a valuable starter in Los Angeles' injury-plagued rotation. Skaggs started a career-high 24 games last season, going 8-10 with a 4.02 ERA. He missed playing time in April this season with a sprained ankle but came back strong.
Skaggs was part of the same Angels draft class as Mike Trout, and they were roommates in the low minor leagues before Skaggs was traded to Arizona. They played on the same team in Cedar Rapids, Iowa, in 2010.
"Words cannot express the deep sadness we feel right now," Trout tweeted Monday evening. "Our thoughts and prayers are with Carli and their families. Remembering him as a great teammate, friend, and person who will forever remain in our hearts ... we love you, 45."
Skaggs' mother, Debbie, was the longtime softball coach at Santa Monica High School. She famously provided postgame tips on his pitching mechanics, even deep into his big-league career.
Skaggs' death is not the first time tragedy has befallen the Angels organization. In April 2009, pitcher Nick Adenhart was one of three people killed when a drunk driver ran a red light and struck a car in which Adenhart was a passenger. The crash took place hours after Adenhart started a game for the Angels against the Athletics and pitched six shutout innings.
The Associated Press contributed to this report.