The DS Techeetah driver takes over as champion from French team mate Jean-Eric Vergne, the winner of Sunday's race. DS Techeetah also clinched the team title.
"I have no words right now...I came so close to giving up so many times, but thanks to the people around me I never did," said da Costa.
Da Costa, 28, has competed in Formula E since the inaugural 2014-15 season but had never previously finished higher than sixth in the standings.
Berlin ePrix
Weekend talking points as De Vries claims maiden world title
15/08/2021 AT 20:47
He joined DS Techeetah for season six from BMW i Andretti and has won three races. (Reporting by Alan Baldwin, editing by Ian Chadband)
Berlin ePrix
'I'm lost for words' - De Vries stunned after Formula E world championship victory
15/08/2021 AT 20:16
Berlin ePrix
'It's really emotional' - New Formula E world champion Nyck De Vries speaks after claiming title.
15/08/2021 AT 20:04