The councillor, who has until now been leader of Liverpool City Council, won the city's first mayoral elections at the first count with 58,448 votes.
It comes after the council voted in February to accept a "city deal" which is set to bring in £130 million of additional government funds.
Mr Anderson was followed in the poll by independent candidate Liam Fogarty with 8,292 votes and Liberal Democrat Richard Kemp with 6,238.
Campaigning for the mayoral elections had been marred this week after candidates from the far-right British National Party and National Front were arrested.
As the result was announced a group of National Front supporters unveiled a banner and then heckled Mr Anderson as he took to the stand to give his acceptance speech.
However Mr Anderson retorted: "We will democratically defeat those fascists at the ballot box every time.
"That is why they shout loudly now, because the people of this city have told them loud and clear: get stuffed."