Valakari started to play football in the youth sector of Käpylän Pallo (KäPa) in 2007. In 2013, he moved to Seinäjoki with his family and joined local club Seinäjoen Jalkapallokerho (SJK). After making his senior debut with the club's reserve team SJK II in a then third-tier level Kakkonen in 2015, Valakari continued his career with Turun Palloseura (TPS). He played with TPS first in the second-tier Ykkönen in 2017, and in the next 2018 season he debuted in the premier division Veikkausliiga. During the first half of the season, he scored four goals in the league.[3]
On 5 August 2018, Valakari signed with the Norwegian club Tromsø,[5] after his father was named the manager of the club's first team.[3]
In January 2020 he moved to Pafos, competing in Cypriot First Division.[6] On 25 November 2022, Valakari extended his contract with Pafos until June 2026.[7] On 18 May 2024, Valakari and Pafos won the 2023–24 Cypriot Cup title, after defeating Omonia 3–0 in the final.[8]
Valakari made his senior international debut for Finland on 11 November 2020, scoring on his debut in a 2–0 victory over France. The other goalscorer was fellow debutant Marcus Forss.[10]
Valakari's father Simo is a former professional player and a Finnish international, and is currently working as a manager of Riga FC. His brother Paavo has also played football professionally.[12] Onni was born in Scotland when his father had a stint as a player at Motherwell.[13][14][15]
On 10 May 2024, it was reported that Valakari had been sentenced to a €9,900 fine in Finnish court for not enrolling to the mandatory conscription service on time in January 2022.[16]