Bryza graduated from Stanford University with a Bachelor of Arts degree in International relations and obtained his Master of Arts in Law and Diplomacy from The Fletcher School of Law and Diplomacy of Tufts University in 1988.
Bryza joined the United States Foreign Service in August 1988. He then served in Poland in 1989-1991 at the U.S. Consulate in Poznań and the U.S. Embassy in Warsaw, where he covered the Solidarity movement, reform of Poland’s security services, and regional politics. From 1991 through 1995, he worked on European and Russian affairs at the State Department. Bryza served at the U.S. Embassy in Moscow during 1995-1997, first as special assistant to Ambassador Thomas R. Pickering and then as a political officer covering the Russian Duma, Communist Party of the Russian Federation, and the Republic of Dagestan in the North Caucasus. He was recalled from Moscow after he allegedly hit a pedestrian in August 1997. From 1997 through 1998, Bryza was special advisor to Ambassador Richard Morningstar, coordinating U.S. Government assistance programs on economic reforms in Caucasus and Central Asia. Starting from July, 1998 he served as the Deputy Special Advisor to the President and Secretary of State on Caspian Basin Energy Diplomacy, coordinating the U.S. Government's inter-agency efforts to develop a network of oil and gas pipelines in the Caspian region.
In April 2001, Bryza joined the United States National Security Council as Director for Europe and Eurasia, with responsibility for coordinating U.S. policy on Turkey, Greece, Cyprus, the Caucasus, Central Asia, and Caspian energy. In June 2005, he assumed duties of Deputy Assistant Secretary of State for European and Eurasian Affairs. He was responsible for policy oversight and management of relations with countries in the Caucasus and Southern Europe. He also led U.S. efforts to advance peaceful settlements of separatist conflicts of Nagorno-Karabakh, Abkhazia and South Ossetia. Additionally, he coordinated U.S. energy policy in the regions surrounding the Black and Caspian Seas and worked with European countries on issues of tolerance, social integration, and Islam.
In August 2009, Armenian National Committee of America (ANCA) Chairman Ken Hachikian sent a letter to Secretary of State Hillary Clinton outlining the concerns of the Armenian American community regarding what he called the recent "biased remarks by Matt Bryza" the U.S. Co-Chair to the OSCE Minsk Group charged with helping to negotiate a settlement of the Nagorno Karabagh conflict.
In May 2010, the White House appointed Bryza as the United States Ambassador to Azerbaijan. On September 21, 2010, the Senate Foreign Relations Committee approved his ambassadorial nomination and sent it to the Senate floor. In a SFRC roll call vote, Democratic Senators Robert Menendez of New Jersey and Barbara Boxer of California who are Armenian Caucus members tried to block the nomination voting against Bryza's appointment. On December 29, 2010 Bryza's appointment by President Obama was confirmed by the White House as a recess appointment. He served as ambassador to Azerbaijan starting from February 2011.