Born in Basingstoke in 1997, Solanke was a star performer for Chelsea under 18's in 2013/14, scoring twice in the final as they won the FA Youth Cup. He was then promoted to the first team squad but only appeared once in 2014-15, as a substitute in a Champions League game. He was prolific in the under-21's though, ending the season with 41 goals in all competitions. Solanke spent 2015/16 on loan at Dutch side Vitesse Arnhem, scoring seven times in 25 appearances. However when contract negotiations broke down on his return to Chelsea he found himself frozen out of the squad in 2016/17, making the matchday squad just once as an unused substitute in a League Cup tie.

At the end of May 2017 Liverpool confirmed that they had agreed a contract with Solanke to join the club on 1 July 2017, with the fee to be decided by tribunal. He finally joined on 10 July after applying the finishing touches to his Liverpool contract. Chelsea were entitled to compensation for his development and valued him at £10million pounds while Liverpool's value was £3m. The clubs reached a compromise that remained undisclosed but a fair bit closer to Liverpool's estimation. He impressed at the Under 20 World Championships in 2017, scoring four goals as England triumphed. He continued this form in pre-season with Liverpool and looked likely to start the season as part of the first team squad as opposed to the under 23's where it was anticipated he be starting off. Though he hadn't established himself in Liverpool's first team, Solanke made his full international debut for England on 14 November 2017 in a 0-0 friendly against Brazil. Sixteen of his 21 league appearances came from the bench and his only goal came on the last day of the season against Brighton.

With both Daniel Sturridge and Divock Origi returning from loan spells, Solanke found himself out of favour in 2018-19 and in the first half of the season made only one matchday squad, against Chelsea in the League Cup when he was an unused substitute. On 4th January 2019, he signed for Bournemouth for a fee of £19 million, having scored just once in 27 appearances for Liverpool. Despite what was a huge fee for Bournemouth, he was not an automatic choice during the remainder of the campaign, with eight of his ten appearances being as a substitute. In 2019/20, Solanke looked like he may go the whole Premier League campaign without scoring, but he finally got off the mark on matchday 35, scoring twice in a 4-1 win over Leicester. Bournemouth were relegated and he remained there for the start of the 2020/21 Championship campaign. He seemed much more comfortable at this level, scoring fifteen goals in forty league appearances in a campaign that saw the Cherries miss out on promotion, losing the play off semi final to Brentford. In 2021/22 he was even more prolific, finding the net 29 times as Bournemouth won promotion back to the Premier League.

Back in the Premier League, Solanke was far more comfortable in 2022/23, scoring six goals and assisting in seven. In 2023/24 he was prolific, starting 37 games and scoring nineteen goals. It brought him to the attention of England manager Gareth Southgate but he was unable to make the squad for Euro 2024. On 9 August, he became the seventh most expensive English player of all time when he agreed to join Tottenham in a deal worth £65 million, of which Liverpool would receive 20% of Bournemouth's profit due to a sell on clause. When fit, Solanke was a first choice striker for Spurs during 2024/25, scoring a respectable nine goals in 27 Premier League appearances and earning his first England cap in seven years. His goals included the opener at Anfield when Liverpool beat Spurs 5-1 to clinch the title on 27 April. He also scored five goals in the Europa League, which Spurs won by beating Manchester United 1-0 in the final in Bilbao.