"I had told the selectors before the tournament started that I won't captain in T20 and they needed to groom someone else for the future," Jayawardene told reporters after the final in Colombo.
Jayawardene, 35, will however continue as a player in the shortest format and will also lead in both Test and one-day cricket.
The accomplished batsman has scored 1,224 runs in 44 Twenty20 internationals at a strike rate of 133.77 per 100 balls.
The first world title for the West Indies since the 50-over World Cup triumph in 1979 also handed Sri Lanka their fourth defeat in a major final since 2007.
Sri Lanka have now lost two successive 50-over World Cup finals in 2007 and 2011 and two World Twenty20 finals in 2009 and 2012.