The 34-year-old confirmed his long-expected departure from Borussia Park this week and will now ply his trade with Liga MX outfit Club Tijuana.
Arango's first club abroad was Monterrey and the Venezuela international will link up with Tijuana's general manager Ignacio Palou, whom he worked under at Puebla.
Cesar Faris, Arango's former national team boss, will be another familiar face for the midfielder as he coaches at Estadio Caliente.
Eberl said it had been a pleasure to have Arango at the club since arriving from Real Mallorca in 2009 but accepted the lure of working with former mentors was too great for the player to resist.
"Now he has the opportunity to link up with his former coach and mentor in Mexico on a longer-term contract, which is something we couldn't offer him.
"We wish him all the best at his new club."
Arango, who has 121 senior caps for Venezuela, made 171 appearances for Gladbach between 2009 and 2014, scoring 31 goals.