Last week the 33-year-old defender rescinded his contract with Valencia a year before it was due to expire, allowing him to move to Qatar without a transfer fee.
The Portugal international had been tipped to return to Porto, the club where he made his professional debut in 2000, but has decided to leave Europe altogether in search of a new adventure.
He has signed a two-year deal with Al-Sailiya, who finished fourth in the Qatar Stars League last season.
Costa enjoyed his most successful years with Porto, winning four league titles as well as the Champions League in 2004 under Jose Mourinho.
He then moved to German side Wolfsburg in 2007 and went on to win the Bundesliga title, before signing for Valencia in 2010 after a six-month loan spell in France with Lille.
Costa did not win any more silverware in Spain but developed into one of Valencia's most important players and became captain at the start of last season following the retirement of David Albelda.