Kamara was born to a Liberian mother. He attended Norcross High School in Norcross, Georgia. He played high school football for the Blue Devils football team. As a junior in 2011, he rushed for 1,300 yards with 17 touchdowns. As a senior in 2012, he rushed for 2,264 yards with 26 touchdowns, and he had 22 receptions for 286 yards and five touchdowns and led his high school to its first state championship. As a result of his successful high school career, Kamara earned Georgia Mr. Football honors from the Atlanta Journal-Constitution, named Class 6A Player of the Year, and earned first-team All-State honors from the Georgia Sports Writers Association. In addition to these accolades, Kamara was selected to participate in the 2013 Under Armour All-America Game.

Coming out of high school, Kamara was considered to be one of the top running back prospects in the nation. He was rated the No. 1 all-purpose back in the 247Composite, the No. 5 player in Georgia, and the No. 42 player nationally in 2012. Rivals.com rated Kamara as the No. 6 player in Georgia.

In 2014, Kamara transferred from Alabama to Hutchinson Community College in Kansas for his redshirt freshman season. In nine games, Kamara ran for 1,211 yards (134.6 per game) with 18 touchdowns and led the Blue Dragons with 1,469 yards of total offense and 21 touchdowns. His successful season with Blue Dragons propelled Kamara to one of the top JUCO prospects in the nation. He earned a 5-star rating from the Rivals.com and Scout.com recruiting networks. He was offered by both Tennessee and the Georgia Bulldogs before ultimately committing to the Volunteers.

In 2015, Kamara transferred to the University of Tennessee to play under head coach Butch Jones. As a redshirt sophomore, Kamara played in all 13 games and shared the backfield with Jalen Hurd and John Kelly. He accounted for 144 yards and two touchdowns in his Tennessee debut against Bowling Green at Nissan Stadium in Nashville, Tennessee on September 5, 2015; his 144 rushing yards set a school record for most rushing yards in a debut game. He became the second Volunteer in history with a rushing touchdown and punt return for touchdown in the same game with a two-yard rushing touchdown and a 50-yard punt return touchdown against Western Carolina. On November 14, against North Texas, he had 15 carries for 127 yards and two touchdowns in the home victory. Tennessee finished with a 9–4 record and qualified for the Outback Bowl against #12 Northwestern. In the 45–6 victory over the Wildcats, he had 53 rushing yards and a touchdown. In the entire 2015 season, he accounted for 698 yards (53.7 yards/game) with seven rushing touchdowns. He averaged 6.5 yards per carry, which was third in the SEC. He was second on team in receptions with 34 for 291 yards and three receiving touchdowns. As a punt returner, he had eight returns for 100 yards (12.5 average) with a touchdown.

In 2016, Kamara was a key contributor for the Volunteers in his redshirt junior season. The running back personnel was the same as the last season for Kamara. In the 2016 Pilot Flying J Battle at Bristol, he had six touches for 34 yards and one touchdown in the 45–24 victory over Virginia Tech. He started his first career game at running back for the Vols in a 28–19 victory over Ohio on September 17. He had 79 all-purpose yards in a 38–28 win against #19 Florida, including six yards on two carries, 12 yards on one reception and career highs of 61 punt-return yards and six punt returns. He had 138 all-purpose yards, including a receiving touchdown, in a 34–31 win against #25 Georgia. He had a career-best game the following week in a 45–38 2-OT loss against #8 Texas A&M at Kyle Field. He rushed for 127 yards and two rushing touchdowns, and had eight receptions for 161 yards and a receiving touchdown. In the next game against #1 Alabama, he was limited to eight carries for 21 yards but had the Vols’ lone touchdown in the 49–10 defeat. He missed some playing time due to being injured. He returned on November 12 in a 49–36 victory over Kentucky. Against the Wildcats, he had 10 carries for 128 yards and two touchdowns. In the 63–37 victory over Missouri, he had 55 rushing yards and two more rushing touchdowns. In the regular season finale against Vanderbilt, he had three total touchdowns (two rushing and one receiving) and 141 scrimmage yards in the 45–34 defeat. In the final game of his collegiate career, he had seven carries for 31 yards and seven receptions for 46 yards in the victory over #24 Nebraska in the Music City Bowl. He finished third in the SEC in touchdowns for the 2016 season.

In 2017, his 728 yards rushing and 826 yards receiving was the first 700/700 season by a Saint, third by an NFL rookie, and the 11th 700/800 season by any NFL player. His 728 rushing yards finished third among rookies behind rushing leader Kareem Hunt and Leonard Fournette. His 81 receptions on the season were first among all rookies and second in the league among running backs behind Le’Veon Bell, and his 826 receiving yards finished first among running backs. Kamara and Ingram became the first running back duo in NFL history to each have over 1,500 scrimmage yards in the same season. Among non-quarterbacks with 100+ carries, his 6.07 yards per rush was the most ever by an NFL rookie, Paul Lowe (1960) and Buddy Young (1948) also achieved this feat, but not as NFL players. Among non-quarterbacks with 100+ carries, his 6.07 yards per rush was the most ever by an NFL rookie, any Saints player, and the third most by any NFL player, trailing Jamaal Charles (6.38 in 2010) and Barry Sanders (6.13 in 1997), since 1980.

In 2017, the Saints finished with an 11–5 record and won the NFC South. In the Wild Card Round against the Carolina Panthers, Kamara had 23 rushing yards, a rushing touchdown, and one reception for 10 yards in the 31–26 victory. In the Divisional Round against the Minnesota Vikings, he had a 14-yard receiving touchdown from Drew Brees in the fourth quarter to put the Saints up 21–20. However, the Saints would lose to the Vikings by a score of 29–24 on the last play of the game. After a spectacular rookie season, Kamara was named the NFL Offensive Rookie of the Year. He was ranked #20 by his fellow players on the NFL Top 100 Players of 2018.