Jayasuriya had been in interim charge since June and on Monday was appointed full-time coach until March 2026 after recent successes, which included a Test match win in England and a home 2-0 Test series sweep against New Zealand.
"The Executive Committee of Sri Lanka Cricket made this decision, taking into consideration the team's good performances in the recent tours against India, England, and New Zealand," Sri Lanka's cricket board said in a statement.
Under Jayasuriya, Sri Lanka also won a one-day international series against India for the first time in 27 years.
Former Sri Lanka captain Jayasuriya was regarded as one of the greatest one-day international batsmen of all time and was pivotal in the 1996 World Cup victory.
Jayasuriya represented Sri Lanka 586 times across the three formats of the game, hitting 42 centuries and taking 440 wickets. He played his last international in 2011.
The former national selector has also had a brush with the International Cricket Council (ICC) anti-corruption unit and was banned from all forms of cricket for two years in 2018.
Jayasuriya was charged after failing to hand over his mobile phones and was accused of obstructing or delaying any investigation into corruption in the game.
He is also an ex-lawmaker and a former deputy minister of the postal service.