Born in Saint-Maur-des-Fossés, Boli began his playing career with Ligue 1 side PSG, joining them when he was eleven years old. He was part of the side's B team from 2005–07. In 2006, he helped their under-18s side to win the French Under-18 Championship and in his last season, he was a top scorer. On 6 May 2008, he scored a 77th-minute winner against Ligue 2 side Amiens SC, in the semi-finals of the Coupe de France to send PSG into the final, where he was an unused substitute as they lost 1–0 to Lyon. On playing for PSG, Boli said, "PSG are the club of my dreams and I joined when I was 11. The fact that I'm now playing here with the first team gives me immense pride." Boli was loaned to newly promoted Ligue 1 side Le Havre AC on 18 October 2008 until the end of the 2008–09 season, making his debut seven days later in a 2–1 home win over Valenciennes at Stade Jules Deschaseaux. He made a total of eleven league appearances, before returning to PSG in July 2009. On 19 August 2009, Boli joined English Championship side Blackpool on trial, with Sky Sports reporting that he could be about to sign a one-year loan deal with the Seasiders. Boli said, "I am happy to be here in England, hopefully it will happen for me." The Blackpool Gazette then claimed it was unlikely Boli would sign, however The Times reported that he was expected to move to Blackpool on loan after a medical planned for 24 August. In September 2011, Boli joined London based football agency Pro Sports Agency. He signed with Bulgarian A PFG club Chernomorets Burgas after a one-week trial period. On 18 February 2013, he was sold to Ukrainian side Zorya Luhansk for a fee of 300.000 €. He signed a two-year contract. On 29 August 2014, Boli was announced as an Anzhi Makhachkala player, signing a four-year contract. In November 2014, Boli was awarded Best Goal of the month and awarded the 1FNL Best Players on the Football National League official website. After joining the club, managed by Sergei Tashuyev, Boli was introduced very slowly into the starting lineup. On his first game against SKA-Energia, he came on as a substitute player for just on 28 minutes. He has scored 26 goals in 62 appearances for the Dagestan based FC Anzhi Makhachkala. On 16 January 2017, Boli signed a two and half years contract with UAE Arabian Gulf League club Al Ain FC. On 18 January 2017, Al Ain decided to void the contract after "additional demands were made by Anzhi and Boli". On 24 February 2017, Boli joined Chinese side Dalian Yifang, and scored 16 goals to promote the team to 2018 Chinese Super League. On 15 March 2018, Boli signed a one-year deal with Major League Soccer side Colorado Rapids. Boli joined Thai League 1 club Ratchaburi Mitr Phol F.C. in the 2019 season. He scored a debut hat-trick on 22 February 2019.
International
Boli holds dual French and Ivorian nationality, and in 2008, ahead of the Summer Olympics in the People's Republic of China, he chose to represent the Ivory Coast. "I'm lucky enough to have dual Franco-Ivorian nationality and I'm proud of my African roots," he said. "I've followed the Elephants a lot in the last few years and I feel there's an interesting situation there. Because of that, I didn't hesitate in choosing that country's shirt." In March 2008, he was called up by manager Gérard Gili to the Ivory Coast Olympics team.
