Atkins was born in Pembroke Pines, Florida on March 28, 1988. He attended St. Thomas Aquinas in Fort Lauderdale and helped his high school football team to be the Class 5A runners-up in both 2004 and 2005. As a junior at St. Thomas Aquinas in 2004, Atkins had 70 tackles (12 resulted in lost yardage), one interception, and four fumble recoveries. In 2005, during his senior season, he had 117 tackles, 7.5 sacks, four forced fumbles, and two fumble recoveries. Following the season, he was named first-team all-county by the Sun-Sentinel and Miami Herald, first-team Class 5A in the state of Florida and was also named Florida Class 5A Defensive Player of the Year. Coming out of high school, he was rated as the 24th best defensive end in the nation by Rivals.com and 41st best by Scout.com.
In track & field, Atkins was one of the state's top performers in the throwing events. In the discus, he got a PR of 48.35 meters at the 2006 FHSAA 3A Region 4, placing 2nd in the finals. At the 2006 FHSAA 3A-4A Outdoor State Finals, he tied for 1st place in the shot put event, recording a top-throw of 18.01 meters.
Atkins enrolled in the University of Georgia, where he played for coach Mark Richt's Georgia Bulldogs football team from 2007 to 2009. He played as a true freshman, recording nine tackles and 0.5 sacks in 11 games.
In 2007, Atkins saw significant playing time as a backup behind Kade Weston and Jeff Owens. On September 21, Owens said of Atkins's impact, "Geno is doing a heck of a job. He's contributing a lot to the defense. He's leading the defensive line in tackles for loss and I think we're tied in tackles." As of September 29, despite being a backup, Atkins was fourth in the Southeastern Conference (SEC) with six tackles for losses along with a sack. On October 6, Atkins was named the starter over Weston and in only his second game led the team in tackles against Vanderbilt. He became the first defensive tackle to lead the team in tackles in a game since Jason Ferguson did so in 1995 and the first defensive lineman since David Pollack in 2003. Following a game against Kentucky in which he had five tackles, he was named SEC defensive player of the week for the week of November 17. Following, his sophomore season Atkins was named First-team All-SEC, and was the only player for Georgia other than running back Knowshon Moreno to be named to the team. During the press conference for Hawaii's quarterback Colt Brennan before the Sugar Bowl, Atkins asked for an autograph and took a photo with Brennan. Fellow Georgia defensive lineman Marcus Howard said of Atkins's antics during the press conference, "He was like acting like a groupie. All of us gave him grief for that." Despite getting Brennan's autograph before the game, Atkins sacked him in the fourth quarter, forcing him out of the game.
Two games into the 2008 season, Atkins already had eight tackles and nine quarterback hurries. After the defense as a whole sacked Heisman Trophy winner Tim Tebow of Florida six times, Atkins said, "I think we rattled Tim Tebow and the offense. We wanted to pressure him. No one really works that well under pressure, not even the greatest quarterbacks. You put a little pressure on them, they're bound to flinch." On November 14 against Auburn, Atkins came in on offense and was the lead blocker for Matthew Stafford on a quarterback sneak. In the Capital One Bowl on January 2, 2009, against Michigan State, Atkins had one tackle and two quarterback hurries.
In 2009, Atkins was listed at No. 5 on Rivals.com′s preseason defensive tackle power ranking. He was also named to the 2009 Outland Trophy watch list. In his three years after his freshman season, Atkins racked up 33 sacks, including 15 as a sophomore and 10.5 as a senior.
Atkins was drafted by the Cincinnati Bengals in the fourth round (120th overall) in the 2010 NFL Draft.
In his second season, Atkins became a full-time starter and led the team in sacks with 7.5, assisting the team to a 9-7 record and a playoff appearance. In the 2011 season, he was tied for number of sacks for a defensive tackle with Oakland's Tommy Kelly. Atkins was named to his first Pro Bowl in his second season as a starter after Vince Wilfork withdrew to participate in the Super Bowl.
In 2012, Atkins recorded 53 tackles, forced four fumbles, set a franchise record with 12.5 sacks, and was selected at a starter in the Pro Bowl as the Bengals made the playoffs for the second consecutive year. After an outstanding 2012, Atkins was regarded as one of the best defensive tackles in the NFL.
On September 2, 2013, Atkins agreed to a five-year, $55 million extension with the Bengals. On October 31, 2013, Atkins tore his ACL in a game against the Miami Dolphins, and missed the rest of the season.
From 2014 to 2016, Atkins started all 16 games each season earning three straight Pro Bowls. He was named First-team All Pro in 2015 and was ranked 29th by his fellow players on the NFL Top 100 Players of 2016.
Atkins married his college sweetheart, Kristen Merritt, on June 25, 2016 at the St. Regis hotel in Buckhead, Georgia.
During his freshman year at the University of Georgia, Atkins learned he suffers from Sickle cell trait.
Geno is the son of former New Orleans Saints and Miami Dolphins safety Gene Atkins.