Chelsea will pay 30 million euros ($33.54 million) for the player, three of which will be based on performance, the Spanish champions said on their website.
Sergio Aguero struck twice as Manchester City moved into second place in the Premier League, two points behind leaders Liverpool, with a 3-1 win at Bournemouth on Sunday. Just three weeks into the new season and last year's top two clubs are already perched at the top of the table.
Pep Guardiola to be a hard task master who will extract the best out of a side that has shone domestically but struggled against Europe's elite.
Eight wins and a draw in their last nine games had seen Leicester emerge as the closest pursuers of runaway leaders Liverpool but they went down 3-1 at the Etihad despite taking an early lead through Jamie Vardy. Images from the English Premier League matches played on Saturday.
Bayern Munich forward Robert Lewandowski took the honours as the league's top scorer with 30 goals after netting in the champions' 3-1 victory over already-relegated Hanover 96.
For the first time in 10 years, four English clubs have reached the quarter-finals of the Champions League
'By giving cameras unimpeded access to their world-class training facilities and coaches, and by showing off Guardiola's genius, All Or Nothing is a striking show of power, a declaration of their conviction of being the bigger club in Manchester,' says Dhruv Munjal.
In Pep Guardiola's 100th match in charge of the Manchester club, captain De Bruyne led from the front as City outclassed the Gunners, who have now suffered six home games without a win. Images from the EPL matches played on Sunday.
The next man in charge faces an unenviable task trying to sort out the existing mess and then living up to goals that seem ever more distant.
News of that transpired on and off the football field
News of all that's transpired on and off the football field.
English Premier League leaders Liverpool will need to maintain their excellent recent record against Everton in Sunday's Merseyside derby if they are to hold their advantage over second-placed Manchester City.
News of all that tranpired on and off the football field.
Barcelona midfielder Xavi raised the King's Cup aloft alongside Andres Iniesta in his final appearance at the Camp Nou on Saturday and now victory in the Champions League would make it a perfect send-off for the club legend.
His first overseas coaching adventure -- Maurizio Sarri has chosen a devilishly difficult league to try and make it happen and a club not exactly known for its patience.
'It's just a big job to do. We wanted to go as far as possible so it was clear at one stage we would face the best teams in the world. City are a special team, one of the best, if not the best team in Europe and they are deserved champions of the Premier League. But it's not about yesterday, it's about tomorrow'
News of all that transpired on and off the football field.
Here are five talking points from the weekend's action:
Barcelona have been drawn to play Pep Guardiola's Bayern Munich in the Champions League semi-finals. The other last-four tie will see Juventus, in their first semi-final since 2003, take on Carlo Ancelotti's Real Madrid, the defending champions.
Bayern Munich's long-time team doctor Hans-Wilhelm Mueller-Wohlfahrt has surprisingly resigned.
Liverpool opened up an eight-point lead at the top of the Premier League with an emphatic and hugely impressive 3-1 win over defending champions Manchester City.
Manchester City begin a crucial week in the Premier League title race when they host Arsenal at the Etihad on Sunday.
The three sides who have bossed the ball the most in Russia, Spain, Germany and Argentina have all said "do-svidaniya" before the quarter-finals.
Manchester United manager Lous van Gaal has again dismissed reports he will leave Old Trafford at the end of the season, saying on Friday he does not have to answer to the media. The Dutchman's future has been the subject of persistent speculation after United's Champions League group-stage exit and indifferent Premier League displays sparked discontent among fans. Former Chelsea manager Jose Mourinho was linked with Van Gaal's job last and United were forced to deny a report that they had met with Pep Guardiola, the Bayern Munich boss who has said he wants to manage in the Premier League next season. "I don't think that the press have to help me with my decisions. First they have sacked me. Now they are interfering with my future. I don't have to answer," Van Gaal told reporters. "I have a relationship with the players of Manchester United. That is the most important thing. "Not everything the media are writing is true."
A summary of Saturday's matches in the Premier League.
"Sergio Aguero will be assessed by Club doctors today after being involved in a road accident on Thursday," City said of the Argentina striker in a statement on their website. (www.mancity.com)
Manchester City coach Pep Guardiola praised Sergio Aguero's natural goalscoring ability after his hat-trick on Wednesday helped defeat Borussia Moenchengladbach 4-0 in their opening Champions League Group C match at the Etihad Stadium.
Rejected former boss David Moyes says Manchester United must not become a club that are continuously sacking managers and should give his under-fire successor Louis van Gaal time to build a successful side.
Tottenham Hotspur routed Bournemouth 5-0 as they leapfrogged City into second place in the league, six points behind leaders Liverpool who thrashed Newcastle United 4-0.
Five talking points from the Premier League weekend:
'I haven't lost any strength in the last four days and in one sense I feel a little relieved but focused on the objectives we set for ourselves at the start of the season'
Manchester City withdrew from the battle to secure the services of Arsenal's Chilean forward Alexis Sanchez, leaving Jose Mourinho's Manchester United as the most likely destination for the 29-year-old.
Real Madrid forward Vinicius Jr. score twice as his side punished a sloppy Liverpool to win 3-1, while Manchester City beat Borussia Dortmund 2-1 in Tuesday's Champions League quarter-final first leg.
Manchester City crushed Watford 6-0 in the FA Cup final on Saturday
News of all that transpired on and off the football field
Van Dijk was substituted early in the game when Everton goalkeeper Jordan Pickford made a reckless challenge in the box, which left Liverpool manager Juergen Klopp fuming.
Pep Guardiola's insatiable team were already thinking beyond the magnificent 2018-19 campaign and contemplating a third straight English title win next season with the Spaniard having said they will get even better.
Images from the UEFA Champions League matches played on Wednesday night.
Bayern Munich striker Robert Lewandowski netted the Bundesliga's fastest hat-trick on his way to a sensational five-goal haul as a halftime substitute in their 5-1 demolition of VfL Wolfsburg on Tuesday.