He defeated Dr Alasdair McDonnell in a vote at the party's annual conference in Armagh by 172 votes to 133.
Foyle MLA Mr Eastwood, 32, is the SDLP's youngest member of the Northern Ireland Assembly and becomes the sixth leader of the party.
South Belfast MLA Fearghal McKinney has been voted the party's new deputy leader.
Mr McKinney received 158 votes, with Upper Bann MLA Dolores Kelly getting 138.
Read more: Colum Eastwood's 10-year rise to SDLP leader
After the leadership result was announced, Mr Eastwood paid tribute to Dr McDonnell, who had led the party since 2011.
"Alasdair has stretched every fibre of his being for this party," he said.
"He is a man who has given the work of two lifetimes for the good of this party and the community he serves."
Mr Eastwood also pledged he would work together as a team with Mr McKinney.
Under his leadership, he added, the SDLP's "principal conversation" would be "about shaping this country for the next 20, 30 and more years".
Among his first tasks as leader will be to make key strategic decisions over continuing negotiations between Northern Ireland's main parties aimed at resolving the current political crisis at Stormont.
Dr McDonnell, the MP for South Belfast, told party delegates he had "given his all and a little bit more" during his time at the helm.
He added: 'I wish to offer Colum every best wish as he continues, I hope, to renew, regenerate and rebuild the party."
Colum Eastwood is the new leader of the Social Democratic and Labour Party (SDLP).