Gomez, a former Major League player, coach, manager, scout and executive, had been working for the Angels for the past 28 years, most recently as a special assistant to the general manager.
He died as a result of complications from injuries sustained when he was hit by a truck while walking to his car during Spring Training in Arizona last March.
"The Angels family has lost one of its invaluable members, and one of baseball's truly great ambassadors," Angels GM Tony Reagins said.
"His influence and impact on so many throughout the industry is impossible to measure. Though he will be missed, Preston's legacy will forever remain a part of this organization."
Gomez made baseball history in 1969 when he accepted the job as the first manager in San Diego Padres history, but he had a long relationship with the game before that.
"The Padres are deeply saddened by the passing of former manager Preston Gomez," San Diego CEO Sandy Alderson said. "Preston made an initial impression in San Diego as the first manager of the expansion Padres. But his lasting impression throughout baseball will be as a dedicated and accomplished lover of the game.
"His professional success was matched by his personal warmth. He had a kind and generous spirit and will be greatly missed."
A native of Havana, Cuba, Gomez began his playing career in 1944 as a 21-year-old shortstop for the Washington Senators, getting a callup when Major League rosters were depleted because of World War II.
Gomez batted .286 in eight games before spending the rest of his playing career in the Minors. His best season in the Minors came in 1951, when he hit .268 with nine home runs and 58 RBIs for Three Rivers (Penn.).
Gomez's managerial career began in the Mexican Winter League, and he then joined the Dodgers' organization, taking a Minor League coaching position.
After that, he spent eight seasons as a Minor League manager in the Cincinnati, Los Angeles Dodgers and New York Yankees farm systems, guiding clubs such as Fresnillo, Mexico City, Havana, Spokane and Richmond. He led the Dodgers' Spokane club to the Pacific Coast League pennant in 1960. Gomez also spent time coaching with Houston and St. Louis.
In 1965, Gomez became the third-base coach for the Dodgers, where he served through four seasons, earned two National League pennants and a World Series title, and touched the lives of many of his colleagues, including legendary former Dodgers manager Tommy Lasorda.
"The man spent his entire life in baseball," Lasorda said.
"He came from Cuba and got the opportunity to work for the Dodgers. Al Campanis gave him an opportunity to be in professional baseball. He managed at least three Major League teams and was a credit to the game. We are very sorry to see him pass away. He wore the Dodger uniform with pride and dignity. He has helped a lot of people in our game and he will be missed."
Gomez left the Dodgers in 1969 to take the helm of the expansion Padres, joining former Dodgers vice president Buzzie Bavasi, and managed the Friars for four seasons. He later managed the Houston Astros (1974-75) and Chicago Cubs (1980), compiling a 346-529 (.395) managerial record in seven seasons.
He joined the Angels' organization in 1981 as third-base coach, a position he held for four seasons (1981-84) before becoming a special assistant to the general manager, the position he held until his death.
"Preston had an incredible passion for baseball and was a mentor for all of us who were fortunate to spend time with him," said Angels manager Mike Scioscia, who invited Gomez to take an active role in instructing during Spring Training every year.
"He will certainly be missed, but I know his presence will be felt every time we take the field because of the knowledge and wisdom that he imparted to us."
Gomez is survived by his wife Elizabeth, brother Jose Gomez, sisters Rachel Valz and Sara Raspall, son Pedro, daughter Elia, step-daughter Claudia Astorga, adopted son Carlos Becerra, and grandchildren Sergio Jr. and Eliana.
Per Gomez's request, there are no funeral or memorial services planned.
Doug Miller is a reporter for MLB.com. Reporter Ken Gurnick contributed to this story. This story was not subject to the approval of Major League Baseball or its clubs.