Al Pacino wrote him to thank him for his performance in the original production of Our Lady Of 121st Street with the LAByrinth Theatre Company of which he has been a member since 1999.

Solis has originated parts in In Arabia We'd All Be Kings and Our Lady of 121st Street, both written by Stephen Adly Guirgis with direction by Philip Seymour Hoffman. He performed at the Cherry Lane Theater's stage in Havana is Waiting by Eduardo Machado. Solis has also been a member of The Actors Studio since 2001, where he has appeared in plays including Salome starring Dianne Wiest and Al Pacino.

Solis has appeared in over 18 films including The Forgotten, Taking Chance, The International, My Soul to Take, and Gun Hill Road (winner of the 2011 Grand Jury Nominee at the Sundance Film Festival). Solis' television appearances include The Following, The Good Wife, Made in Jersey, NYC 22, Weekends at Bellevue, Criminal Minds, Army Wives, ATF-The Line, Damages, Fringe, The Sopranos, Oz, The West Wing, Third Watch, NYPD Blue, New York Undercover, and Blue Bloods.

In 2013 Solis co-created a film production company called Subway Token Films with his partner, Actress Liza Fernandez. Their first short film, Tinto, shot on location in the Maipo Valley wine region of Chile, South America, premiered at the Tribeca Film Festival in 2014, getting nominated for Best Short Narrative. It also screened at the Shnit Worldwide Short Film Festival in 2015. Their next short film, iHeart (which Solis directed), made its world premiere at the Hoboken International Film Festival; it won the Award of Merit at One-Reeler Short Film Competition, and continues its way through the festival circuit. His next short film, Going Down was shot in Los Angeles in June and is in post-production. He is an active volunteer at the 52nd Street Project, a non-profit group that matches inner-city kids with professional theatre artists to introduce them to the Business and craft of theatre production. He is also a supporter of the ASPCA and WSPA.

Solis had a recurring role on The Following. He was a regular on the CBS TV series Made in Jersey starring Kyle MacLachlan, and Janet Montgomery. On the same network he played Sgt. Terry Howard on NYC 22, produced by Jane Rosenthal and Robert De Niro, as well as a recurring role on The Good Wife as the "No-Nonsense" Det. Kevin Rodriguez. Solis also landed a role on USA’s Colony playing Geronimo, and ABC’s The Family playing Editor-in-Chief Gus Flores. Felix was recently cast in the series regular in ABC’s Ten Days in the Valley as Commander Gomez that premieres in October 2017.