They are two institutions that share a number of connections, largely started by Johan Cruyff, who played for and managed both teams.
Below, Sports Mole has picked out five footballers who spent time at the Amsterdam ArenA and Camp Nou during their careers with varying degrees of success.
The former Arsenal winger joined Ajax in 1992 and soon became a key fixture in the starting lineup, culminating in him featuring as de Amsterdammers won the 1995 European Cup at the expense of AC Milan. He would go on to join Arsenal in 1997, but three years later the Dutch international was transferred to Barcelona for £25m. He spent four years with the Catalan outfit, but failed to inspire any trophy success.
Major Ajax honours: Three league titles, one Dutch Cup and one Champions League
Major Barcelona honours: None
Never one to shy away from controversy, Ibrahimovic's spells with both clubs were incident-packed. He signed for Ajax in 2001 from Malmo, but it took him time to win over the supporters. In fact, when he left three years later, some of the Dam faithful were not disappointed to have seen the back of him. Spells with Juventus and Inter Milan followed, before he made a big-money move to Barcelona in 2009. He cost the Spanish giants a reported £60m, but Pep Guardiola seemingly was uncertain as to where he fitted in alongside Lionel Messi. After one season, Barca cut their losses and offloaded the Swede to AC Milan.
Major Ajax honours: Two league titles, one Dutch Cup
Major Barcelona honours: One league title, one World Club Cup, One European Super Cup
Like Overmars, Litmanen was part of the Ajax side of the mid-1990s which captured many people's imagination. He became an Ajax player in 1992 and scored over 100 goals, including nine on their run to the 1995 Champions League success. Such form and statistics saw him reunited with Van Gaal at Barca in 1999, but injuries hampered the Finn from the outset. When Van Gaal was sacked in 2000, Litmanen was frozen out and even lost his number 10 shirt to Rivaldo. He moved to Liverpool in 2001, before going on to spend a further two more seasons at Ajax in the autumn of his career.
Major Ajax honours: Four league titles, three Dutch Cups and one Champions League
Major Barcelona honours: None
Having impressed in Italy with Lazio and Juventus, Laudrup switched to Barcelona in 1989. The Dane would become a pillar of Cruyff's 'Dream Team'. However, he would lose a lot of respect from the Catalans when in the summer of 1994, he switched to bitter rivals Real Madrid. He would end his career in Amsterdam, winning two trophies in the process.
Major Ajax honours: One league title, one Dutch Cup
Major Barcelona honours: Four league titles, one Spanish Cup, one European Cup
While the Ajax side that won the European Cup in 1995 was widely regarded to have been a fantastic team, many felt that Kluivert was the jewel in the crown. He came off the bench in the final to score the winning goal, as well as finding the net against rivals Feyenoord. After a failed move to AC Milan in 1997, 12 months later he joined Barcelona, where he would rediscover his clinical touch. He spent six seasons in Spain and when he left on a free transfer for Newcastle United, he had scored 120 goals.
Major Ajax honours: Two league titles
Major Barcelona honours: One league title