It marks a return to Europe's biggest club competition after a year playing in the Europa League, having missed out on qualification during Antonio Conte's final season on the bench in 2017-18.
The Blues cemented their position inside the top four at the weekend with a 3-0 victory over Watford, with Ruben Loftus-Cheek, David Luiz and Gonzalo Higuain all on target.
Maurizio Sarri's men fulfilled expectations on the pitch in their penultimate game of the season, but also benefitted from their rivals' failings to take the spot with a match to spare.
Tottenham were upset by Bournemouth in a 1-0 defeat on Saturday after being reduced to nine men, while the following day Arsenal and United were also frustrated by opponents situated firmly in the bottom half of the table.
The Red Devils drew 1-1 with already relegated Huddersfield after throwing away an early lead, a result later mirrored by the Gunners who were held by lowly Brighton.
Pierre-Emerick Aubameyang had given his side the advantage at the Emirates Stadium with a ninth-minute penalty, only to see Brighton - whose own relegation concerns were vanquished the previous day thanks to defeat for Cardiff City - hit back via Glenn Murray.
Those results mean that Chelsea now sit four points ahead of Arsenal and five clear of United, an unassailable points difference ahead of the final round of fixtures next Sunday.
Tottenham too know that they are almost certain to be in the Champions League next season, although Arsenal still mathematically have a chance.
Three points clear of their north London rivals and with an advantage in goal difference of eight, only a heavy defeat at home to Everton and a simultaneous big win for the Gunners at Burnley would see Mauricio Pochettino's charges relinquish fourth place.
Arsenal, meanwhile, may yet have another route open to the Champions League, if they finish the season as Europa League champions.