As the son of recent Scottish immigrants James and Alexandrina Webster, Alex Webster grew up in Kearny, New Jersey, where he attended and played high school football at Kearny High School. Webster played a key role on Kearny High School’s football team which won the 1948 New Jersey High School State Championship. In spite of losing a father to cancer at an early age in 1941, Webster and his younger brother James, rose up with the help of uncles and aunts and excelled in football earning college scholarships. As a senior at Kearny High School in 1948, Alex Webster was offered a full-ride scholarship from NFL legend Beattie Feathers to play college football at North Carolina State University.

Webster was drafted in the eleventh round of the 1953 NFL Draft by the Washington Redskins, but chose to play professional Canadian football for the Montreal Alouettes from 1953 to 1954. While in Canada, he was named an All-Star in 1954 and played in that year’s Grey Cup.  In 1955, Webster returned to the United States and played for the New York Giants from 1955 to 1964. In his first year with the Giants, Webster led the team in rushing with 634 yards. While with the Giants, he rushed for 4,638 yards, caught 240 passes for 2,679 yards, and scored 56 touchdowns (39 rushing and 17 receiving). He was named to the Pro Bowl twice, in 1958 and 1961. With 336 points, Webster is 10th on the Giants’ career scoring list.

In 1956, Webster played in the NFL championship game against the Chicago Bears featuring Hall of Fame players and coaches. Webster scored two touchdowns in the second half and contributed with 103 all-purpose yards. The game came to be known as the second “Sneakers Game” because the Giants chose to play in high-top Chuck Taylors due to icy field conditions. The Giants won the game 47-7.  Sportscaster Marty Glickman coined the phrase “a couple of three yards” when describing Webster’s running style.

Webster was considered as one of the “all-time great Giants” and in 2011, was inducted into the New York Giants’ “Ring of Honor”. Alex Webster, LB Brad Van Pelt and Carl Banks, TE Mark Bavaro and P Dave Jennings headlined as the second class of the Giants’ Ring of Honor inductees.   Webster stated that this honor was among the proudest moments of his life. Webster made his last public speech addressing 80,000 fans in attendance accompanied by his grandsons.  Webster is further honored in the New York Giants’ Legacy Club where his vintage #29 game jersey, as well as many historic photographs are displayed.

Webster eventually became an assistant Giant coach under Allie Sherman, and he was later promoted to head coach (1969–1973). He was named UPI NFL Coach of the Year in 1970, as the Giants finished 2nd in the NFC East with a 9–5–0 record. But a 2–11–1 record in 1973 forced him to resign as the Giants head coach. His overall Giant coaching record was 29 wins, 40 losses, and one tie.  Webster married Louise Eggers in 1952, and had two children—Debra and James—, four grandchildren—Kyle, Craig, Tammy and Alexis—, three nephews—Mark, David, Todd—, and a niece—Kristen. Webster also had four grand nieces: Elena, Alexandra, Alexandrina, and Maryn.

After retiring from the NFL, Webster worked in sales and public relations for Nabisco until the early 1990s. Webster also worked in public relations for the Dianah Shore Golf Classic, appearing with former athletes and celebrities such as Joe DiMaggio, Willie Mays, Charley Conerley, Frank Gifford, Bob Hope, and President Gerald R. Ford. Webster served as an announcer for the New York Giants radio broadcast.  On January 27, 1977 at Toots Shore’s funeral, Webster served as an honorary pallbearer along with Pete Rozelle, Art Rooney, Bowie Kuhn, Frank Gifford, Walter Cronkite and Howard Cosell.

Webster owned two restaurants after retiring from the NFL. His first restaurant was called The Stadium, located in Sea Girt, New Jersey. The interior was decorated with sports memorabilia from the New York Giants, New York Yankees and other professional teams. The other restaurant was called Alex Webster’s and located in Tequesta, Florida.  Webster appeared on the gameshow Password which aired on March 16, 1964 with team mate Frank Gifford & actress Betsy Palmer (Season 4, Episode 48).