The 21-year-old has plied his trade in red and white for the past 15 years but leaves without having made a competitive first-team appearance for the Gunners.
Olayinka made the bench in the Europa League and Community Shield for the Gunners and was also loaned out to Northampton Town and Southend United during his time in North London.
Olayinka began the 2022-23 season in bright fashion at Under-21 level, coming up with two goals and four assists from his side's opening four Premier League 2 matches.
However, the Englishman has now ended his lengthy stint with Arsenal and has penned a permanent deal with Cheltenham as he aims to make a name for himself in the senior game.
Olayinka did feature under Unai Emery in Arsenal's 2019 pre-season period, and he was an unused substitute against Standard Liege in a Europa League group-stage draw later that year.
The midfielder follows fellow academy members Omari Hutchinson, Jordi Osei-Tutu, Zak Swanson and Daniel Ballard out of the Emirates on permanent deals this summer.
Sparta Rotterdam 
AZ Alkmaar 
Southampton 
Liverpool 
Como 
Fiorentina 
Sevilla 
Rayo Vallecano 
Ajax 
Pec Zwolle 
Palermo 
Sampdoria 
Ipswich 
Manchester Utd 
Napoli 
Roma 
Moreirense 
FC Porto 
Leganes 
Real Madrid 
Lazio 
Bologna 
Empoli 
Udinese 
CSKA Moscow 
Rubin 
Slovan Bratislava 
AC Milan 
Sparta Praha 
Atletico Madrid 
Valencia 
Barcelona 
Stade Brestois 29 
Bayer Leverkusen 
Red Bull Salzburg 
Bayern Munich 
Paris Saint Germain 
Inter 
RB Leipzig 
Manchester City 
Feyenoord 
Sporting CP 
Arsenal 
FC Rostov 
Spartak Moscow 
Aston Villa 
Juventus 
Celtic 
Club Brugge 
Dinamo Zagreb 
Borussia Dortmund 
Monaco 
Benfica 
PSV 
Shakhtar Donetsk 
Lokomotiv Moscow 
Dinamo Moscow