Barca were 3-0 up by half-time, Robert Lewandowski scoring his 20th league goal of the season before Alejandro Balde, 19, doubled the lead.
Lewandowski added the third before Jules Kounde’s header made it 4-0.
Espanyol did reduce the deficit through Javier Puado and Joselu but remain in trouble near the bottom of the table.
Barcelona have 85 points, 14 more than nearest rivals Real Madrid, with 12 points left to play for.
It is their first La Liga title since club legend Lionel Messi left in August 2021 and first since Xavi was appointed manager in November 2021.
Meanwhile, Espanyol are in danger of a second relegation in four seasons from La Liga after a ninth league defeat in 11 games.
They are four points from safety with four matches left.
Xavi delivers in first full season
Barcelona’s players will have to wait to get their hands on the trophy but they celebrated after the full-time whistle before making a hasty retreat to the dressing room after some Espanyol fans dashed on to the pitch.
Barca trailed Real Madrid by three points after losing 3-1 away to them on 16 October, while they made a disappointing exit from the Champions League after losing three of their six group games.
But Xavi, who won eight La Liga titles during a distinguished 17-year career playing in Barca’s first team, has delivered in his first full season in charge.
It was a particularly emotional night for captain Sergio Busquets, who has confirmed he will leave Barcelona at the end of the season after 18 years at the club.
This is the 34-year-old’s ninth league title with Barca but the future looks promising for the side, with Balde and Kounde scoring their first La Liga goals in Barcelona colours.
Barcelona will move out of their Nou Camp home next season while the stadium is redeveloped.
But fans will get a chance to celebrate the club’s first major trophy since 2020-21 during their last two home games – against Real Sociedad on Saturday and Mallorca on 28 May.
