Tyms played college football at Florida A&M University for the Rattlers.
Tyms went undrafted in the 2012 NFL Draft. During the 2012 preseason, Tyms was on the practice squad for the San Francisco 49ers.
In September 2012, Tyms signed with the Miami Dolphins off the 49ers' practice squad. With the Dolphins, Tyms traveled to New England during the final week of the 2012 regular season.
On October 22, 2013, Tyms signed with the Browns. After spending time on the practice squad, Tyms was elevated to the active roster on December 4, 2013, after defensive end Desmond Bryant was placed on the non-football illness list.
On July 27, 2014, Tyms signed with the New England Patriots. On August 7, in a preseason game against the Washington Redskins, Tyms scored his first touchdown as a Patriot. Additionally, he caught 5 passes for 119 yards. After the preseason, Tyms was informed he would be on the 53-man roster following his suspension in April. Tyms was activated to the 53-man roster on October 6, 2014. Tyms scored his first NFL touchdown on October 12 on a 43-yard pass from Tom Brady. Prior to the touchdown, Tyms had two career NFL receptions for 12 yards. Although he was inactive Tyms earned a Super Bowl ring as the Patriots defeated the Seattle Seahawks 28-24 in Super Bowl XLIX.
Tyms was placed on the Patriots' injured reserve on August 25, 2015 and the Patriots did not tender him a contract at the conclusion of the league year.
On April 7, 2016, Tyms signed with the Indianapolis Colts.
On October 24, 2016, Tyms was signed to the Hamilton Tiger-Cats' practice roster. Tyms played in the final game of the regular season and the Tiger-Cats' lone playoff game. In his one regular season game he caught 4 passes for 33 yards with 1 touchdown. He had a breakout performance in the Eastern Division Semi Final against the Eskimos, catching a game high 8 passes for 114 yards. Nevertheless, the Tiger-Cats were defeated 24-21, thus ending their 2016 season.
On September 14, 2017, Tyms was signed to the Toronto Argonauts practice roster.
Tyms was born in Kent, Washington, he was raised as a foster child, growing up in Fort Lauderdale, Florida.