Alvarez was born in Cuba in 1950, the youngest of Licinio and Isola Alvarez's three sons. Alvarez's father Licinio had been a successful lawyer in Cuba, but his parents fled to the United States to escape Fidel Castro's communist revolution in 1960, when Alvarez was a 10-year-old boy. He was raised in Miami, Florida and attended North Miami Senior High School in North Miami, Florida, where he was an all-county high school football player for the North Miami Pioneers. Alvarez was the Pioneers' star halfback who could run and catch, and was touted by the local newspapers as the best back in Dade County—on offense and defense. On at least two occasions, he played all forty-eight minutes of a high school game, playing on both offense and defense. He was highly recruited by multiple universities, including the hometown University of Miami and the University of Florida, but he ultimately chose Florida where his older brothers Arturo and Cesar were already enrolled. Alvarez graduated from North Miami High School in 1968.
After graduating from high school, Alvarez accepted an athletic scholarship to attend the University of Florida in Gainesville, Florida, and played for coach Ray Graves and coach Doug Dickey's Florida Gators football teams from 1969 to 1971. During Graves' final season as Florida's head coach in 1969, Alvarez was one of several talented second-year Gators known as the "Super Sophs" who led the team to its then all-time best record of 9–1–1. At the close of his sophomore season, he was honored as a first-team All-Southeastern Conference (SEC) selection and a consensus first-team All-American, and he caught a nine-yard touchdown pass to provide the Gators' margin of victory in their 14–13 upset of the Tennessee Volunteers in the 1969 Gator Bowl. Alvarez was known for his speed on the football field, and the media dubbed him the "Cuban Comet." He was also the Gators' leading receiver in 1970 and 1971, marking three straight seasons as the Gators' top offensive weapon. Alvarez was also a first-team Academic All-American in 1969 and a second-team Academic All-American in 1970 and 1971, and was chosen for the Academic All-American Hall of Fame in 1991.
Although Florida has fielded many prolific offenses including 17 All-American receivers and two Heisman Trophy-winning quarterbacks since Carlos Alvarez last played in 1971, he is still the Gators' record holder for pass receptions in a single game (15), in a single season (88), and career receiving yards (2,563)/ At the end of his three-year college career, Alvarez held many Gator and SEC pass receiving records, including career, season and game pass receptions and yardage records. His career record of 176 receptions was broken by Andre Caldwell in 2007, and he ranks second in Gator history (and third in SEC history) in receiving yards in a single season (1,329 yards in 1969) and second on the receiving yards charts in a single game (237 against Miami in 1969). He ranks ninth among all-time Gators receivers in career touchdown receptions (26), seventh in touchdown receptions in a single season (18), and is tied for third for most touchdown receptions in a single game (3). His 133 yards per-game average in 1969 is still the all-time single-season best among Gators, and has only been exceeded once in the SEC.
Alvarez ranks second among Gators receivers with thirteen games for 100 yards or more receiving, one behind career leader Jabar Gaffney. He ranks first among Gators for most 100-yard receiving games in a season, also tied with Gaffney and Travis McGriff, all with eight. Alvarez achieved this in 1969 when six of those 100-yard games were achieved consecutively—also a team record he shares with two other Gators.
Alvarez graduated from the University of Florida with a bachelor's degree in political science, with honors, in 1972. The Dallas Cowboys selected him in the fifteenth round (390th overall pick) of the 1972 NFL Draft, but he did not play or sign a contract because of chronic knee injuries. He received an NCAA Post-Graduate Scholarship Award to attend the Duke University School of Law in Durham, North Carolina, and earned his juris doctor (J.D.) degree summa cum laude in 1975. After graduation, he worked as a law professor at the Southern Methodist University School of Law in Dallas, Texas, where he was named the Outstanding Law Professor in 1980.
Following in the family legal tradition of his father and older brothers, Alvarez became a practicing attorney. He is a member of The Florida Bar, and has been admitted to practice before the U.S. District Court for the Northern District of Florida, the U.S. Court of Appeals for the Eleventh Circuit, and the U.S. Court of Claims. He has served on the Florida Elections Commission and Second Judicial Circuit Nominating Commission, and was awarded the Jose Marti Award for Outstanding Achievement in the Cuban Community from the U.S. Department of Health, Education and Welfare. Alvarez is an environmental and land use attorney based in Tallahassee, Florida, but his current practice emphasizes mediation, arbitration and alternative dispute resolution.
Alvarez was inducted into the University of Florida Athletic Hall of Fame as a "Gator Great" in 1986, and elected to the College Football Hall of Fame in 2011. In one of a series of articles written in 2006, The Gainesville Sun recognized him as No. 7 among the top 100 all-time Gators football players from the first 100 years of the team.