Under Frank de Boer, the Dutch giants shocked Barcelona at the Amsterdam ArenA, while they nearly eliminated AC Milan after draws at home and away.
It was domestically that they impressed most, though, as they not only won their fourth consecutive Eredivisie title, but also made it to the final of the KNVB Beker, regardless of the loss of star players Christian Eriksen and Toby Alderweireld.
Below, in alphabetical order, are Goal's three nominees for Ajax's player of the season, based on their club performances in all competitions. Cast your vote in the poll at the bottom of the article.
Daley Blind might have struggled to find his best form in the opening weeks of the 2013-14 campaign, but he hugely impressed after head coach Frank de Boer opted to switch him from left-back to the position of holding midfielder.
The 24-year-old had mainly featured in defence since breaking into the first team in Amsterdam, but playing in midfield was by no means a novelty for Blind after being fielded in the middle of the park regularly during his years at the club's youth academy and he proved De Boer right for moving him higher up the pitch with some fine performances.
He not only played a pivotal role in Ajax's successful season with his strong defensive displays, providing his side's back four with excellent cover whenever needed and intercepting numerous balls in midfield, but also contributed plenty in possession.
Blind might have scored just once all season, but his accurate passing was often at the heart of Ajax's attacking play and he rarely lost possession.
Jasper Cillessen started the season as back-up to Kenneth Vermeer, but he didn't need long to show De Boer that he ought to be Ajax's No.1 and his head coach will have no regrets over his decision to switch goalkeepers.
The 25-year-old kept a clean sheet in his first two Eredivisie games after dethroning Vermeer and eventually went on to an impressive 18 clean sheets in 40 games in all competitions, thus earning himself a spot in Netherlands' World Cup squad.
Fine performances in the Champions League games versus Celtic and Barcelona helped Ajax secure third spot and qualification for the Europa League, while he was equally impressive in vital league matches against PSV and Feyenoord.
Cillessen might not be the most spectacular goalkeeper, but the way he commands his area, positions himself and always keeps his calm on the ball make him the perfect shot stopper for Ajax.
Lasse Schone was regarded as the perfect back-up when he joined Ajax from NEC in the summer of 2012, but the Denmark international has shown this season that he is so much more than just the ideal substitute.
The versatile midfielder was often employed as right-winger, but also featured in pretty much each position in midfield and even made a few appearances in defence.
Regardless of his position, Schone never let De Boer or his team-mates down as he always gave his all and he made the difference for Ajax on more than one occasion, most notably in the Champions League win over Celtic.
The No.20 arguably got one of the best assists of the season, too, with his brilliant pass for Kolbeinn Sigthorsson in Ajax's 1-0 win over PSV and there's not one coach who would not like to have a player with Schone's attitude and workrate in his team.