Vela attended Saint Joseph Academy in Brownsville, Texas. After graduating from Georgetown University in Washington, D.C., he attended the University of Texas School of Law. His interest in public service grew from his work helping individuals seek justice in state and federal courts as an attorney for more than 20 years in South Texas.

Congressman Vela is a member of the House Agriculture Committee, where he serves on the General Farm Commodities and Risk Management Subcommittee and the Subcommittee on Conservation and Forestry. Vela joined the panel in 2013 at the beginning of his first Congressional term and served as the Vice-Ranking Member of the full committee during the 115th Congress. He was the only Texas Democrat appointed by the House of Representatives' Leadership to serve as a negotiator on the Conference Committee which drafted the 2014 Farm Bill, and was closely involved in its reauthorization in 2018. The Farm Bill is a comprehensive law which sets agriculture policy and funding for nutrition programs, including food stamps, for the next five years. Congressman Vela also sits on the House Armed Services Committee, where he has fought to ensure that U.S. servicemembers are prepared to respond to a range of military operations. He is committed to ensuring that servicemembers and their families have access to housing, healthcare and basic living necessities to sustain them through the challenges of military service. Congressman Vela is a member of the Subcommittee on Seapower and Projection Forces and the Subcommittee on Intelligence and Special Operations.

In addition to his committee assignments, Congressman Vela is also the Deputy Head of the United States Delegation to the North Atlantic Treaty Organization (NATO) Parliamentary Assembly (PA). The NATO PA is comprised of over 250 delegates from 30 NATO countries who provide oversight of NATO operations and act as a conduit between the alliance and legislators of member countries.

In Congress, Vela has been a strong advocate for immigrant rights, education programs-including Head Start and Pell Grants for college students-and community health centers. He is vehemently opposed to the construction of a border wall and is focused on bringing peace and security to our neighbors in Matamoros and Reynosa. He is also working to bring jobs and economic development to South Texas through many efforts, including transforming the Port of Brownsville into a competitive deep water port. Congressman Vela is married to Rose Vela, a former Justice on the Texas Court of Appeals, and they reside in Brownsville, Texas.