Welker started his football career at Heritage Hall School in Oklahoma City, where he and Graham Colton were teammates. In his junior year, he helped lead his team to the 2A State Football championship over Tishomingo High School; in that game, Welker had three touchdowns, over 200 all-purpose yards, a 47-yard field goal, and an interception. Also, in 1999 he was named The Daily Oklahoman All-State Player of the Year, and Oklahoma State Player of the Year by USA Today. Welker played in the 2000 Oil Bowl, scoring a 40-yard field goal for the Oklahoma team. Out of high school, Welker was not recruited much as he was considered to be too small to play at the college level. However, after a recruit at Texas Tech backed out of his scholarship, it was offered to Welker.

At Heritage Hall, Welker was a prolific contributor on offense, defense, and special teams. As a running back, he scored 80 touchdowns (53 rushing and 27 receiving). As a defensive back, he had 581 tackles, 22 interceptions (three of which he returned for touchdowns), and nine fumble recoveries. As a kicker, he scored 35 field goals and 165 extra points; his longest field goal, 57 yards, actually exceeds the personal best of current Patriots kicker Stephen Gostkowski.

Welker's last minute signing proved to be a bonanza for the Texas Tech Red Raiders. Based on a highlight reel from high school, Welker earned the nickname "The Natural" before his freshman year for his versatility and big-game performances. Over his four-year career, he had 259 receptions for 3,019 yards and 21 touchdowns, and 79 rushes for 456 yards and two touchdowns. He also scored eight touchdowns returning punts in his career, still tied for the NCAA record. In 2003, Welker won the Mosi Tatupu Award, given annually to the best special team player in college football.

After his senior season at Texas Tech, Welker went undrafted in the 2004 NFL Draft but ended up signing as a free agent with the San Diego Chargers. Despite making the Chargers' roster out of training camp, Welker was cut after the first week of the 2004 season and signed with the Miami Dolphins, where he was mostly used on special teams. Playing against the Patriots on October 10, 2004, Welker became the second player in NFL history to return a kickoff and a punt, kick an extra point and a field goal, and make a tackle in a single game.

During training camp at the beginning of the 2005 season, Welker was promoted to the third wide receiver spot after Chris Chambers and Marty Booker. He finished the season with 29 receptions for 434 yards and no touchdowns. He also had 43 punt returns for 390 yards, a 9.1 average, and 61 kickoff returns for 1,379 yards, a 22.6 average. These ranked 11th and 20th in the NFL, respectively.

After rumors that he would be cut during the 2006 preseason, Welker started off being the lone bright-spot of the struggling Miami Dolphins offense. Through five games, he netted a team-high 29 catches and team-high 299 yards.

In his first two postseason games, Welker had 16 receptions for 110 yards and two touchdowns. He tied the Super Bowl record of 11 receptions in a single game in the Patriots' 17-14 loss to the Giants in Super Bowl XLII.