Loan to Stade Rennais

On 31 August 2015, Boga joined Rennes on a season-long loan to gain first team experience since his impressive spell in the Chelsea youth system.^[6] He made his debut on 18 September, as an 82nd-minute substitute for Paul-Georges Ntep in a 1–1 draw with Lille in Ligue 1.^[7] At the beginning of October, Boga made a single appearance for Rennes' reserve team against GSI Pontivy, in which he scored the only goal of the game, converting a penalty in the first-half.^[8] On 28 November 2015, in his first start for the team, Boga scored his first professional goal, against Stade de Reims which resulted in a 2–2 draw.^[9] His second goal of the season took the Round of 64 Coupe de France match against OGC Nice into extra time. The game went to penalties, and Rennes won the shootout 7–6.^[10] On 9 January 2016, Boga scored his third goal of the season in a 2–2 draw with Lorient.^[11]

Loan to Granada

On 6 July 2016, Boga joined La Liga club Granada on a season-long loan.^[12] He made his Granada debut on 20 August in a 1–1 draw with Villarreal, playing the full 90 minutes.^[13] A week later, Boga scored his first goal in a 5–1 home defeat against Las Palmas, scoring Granada's equalizer after Las Palmas took the lead through former Liverpool player Nabil El Zhar.^[14] On 2 April 2017, Boga scored the equalizing goal against Barcelona. Granada lost the game 4–1.^[15]

Chelsea debut and loan to Birmingham City

Boga returned to Chelsea for the 2017–18 season and unexpectedly started in their first game of the season against Burnley. However, he was substituted in the 18th minute after Gary Cahill was sent off.^[16] He signed a new three-year contract with Chelsea before, on 28 August 2017, joining Championship club Birmingham City on loan for the 2017–18 season.^[17]

He was one of six debutants in Birmingham's next fixture, away to Norwich City. He played the whole match as his team lost 1–0,^[18] and continued in the side for the next five league matches. Incoming manager Steve Cotterill imposed a fitness programme on the players, and on Boga in particular, who did not start another match for two months.^[19] When he did return, in a 1–1 draw away to Sheffield United on 25 November, he opened the scoring with his first goal for Birmingham. After the defence failed to clear a corner, "an unmarked Boga jinked on the edge of the area before thumping a curling effort past Blackman's outstretched hands";^[20] the goal won him the club's Goal of the Season award.^[21] Two weeks later, with his side losing 1–0 away to Fulham with 15 minutes left, he missed a penalty, hitting his shot too high.^[22] Cotterill continued to select Boga, and he scored his second Birmingham goal with a powerful header in a 3–1 win against Sunderland in late January that lifted his team out of the relegation positions.^[23] He played less under Cotterill's successor, Garry Monk, and not at all in the last few weeks of the season, as Birmingham narrowly avoided relegation.^[24] In all competitions, he made 34 appearances, 25 of which were starts.^[25]