The fee is £19.6m (€23m) but with add-ons could rise to £22.7m (€26.5m) with the deal also thought to include a 10 per cent sell-on fee.
Bassey has signed a contract with Ajax until June 2027 and arrived in Austria on Wednesday to join the Dutch champions’ training camp.
His departure will see Rangers pocket a club-record fee for a player that cost them a mere £230,000 from Leicester two years ago. Rangers sold academy graduate Nathan Patterson to Everton in a deal worth up to £16m in January.
“Rangers Football Club can confirm Calvin Bassey has joined Ajax in a deal which is the largest in Rangers’ history,” a club statement read
“Calvin leaves with best wishes from everyone at Rangers and we thank him for his hard work and commitment over the past two seasons.
“The 22-year-old joined Rangers from Leicester City for a Training Compensation Fee in the summer of 2020, making 65 appearances for the Light Blues.
“Bassey played his part in Rangers’ historic 55th league title victory, won the 2022 Scottish Cup, while also having a huge role in the incredible UEFA Europa League run to the final in Seville last season.
“We wish Calvin all the best for his future career.”
Bassey made 50 appearances across all competitions last season and was named in the Europa League team of the season following Rangers’ run to the final.
He also played a key role as the club won the Scottish Cup in May, adding to the Scottish Premiership title he won the previous campaign.