Saul is Chelsea's second signing of the summer after spending a club record £97.5 million ($134 million) to re-sign Romelu Lukaku from Inter Milan.
Antoine Griezmann, 30, who scored 133 goals in his first spell with Atletico, has rejoined on a one-year loan deal with an option to extend by another year
United announced on Friday a deal had been struck with Juventus to bring the five-time Ballon d'Or winner back to Old Trafford for a fee that could rise to 23 million euros.
Real are understood to have made two bids for Mbappe last week - and there were reports on Tuesday they were prepared to go to 200 million euros - but PSG decided they would rather not sell, and risk losing the France forward for free
Midfield prodigy Camavinga, who is just 18, penned a six-year deal at the Santiago Bernabeu with Real reportedly paying a fee of 31 million euros ($36.6m) plus nine million euros more in bonuses.
Carlo Ancelotti said that Real Madrid were not interested in the return of Ronaldo who fired the club to four Champions League triumphs.
Funded for a decade by Qatari sovereign wealth, PSG is one of the few clubs in the world that can afford the 34-year-old Messi's salary.
Premier League: Manchester City sign 'natural talent' Jack Grealish from Aston Villa in reported £100 million deal
The fee shattered the previous British record of £89 million paid by Manchester United to sign Paul Pogba from Juventus in 2016.
No fee has been disclosed but British media reported value the deal at £34 million ($47 million) rising to £48 million with add-ons.
He scored two goals in 21 games in Madrid before joining Milan last season on loan, scoring seven goals in 39 appearances for the northern Italian outfit.
Serie A: AC Milan director Paolo Maldini confirms Olivier Giroud's arrival, regrets Gianluigi Donnarumma exit
Olivier Giroud, a World Cup winner, is reported to be set to sign a two-year contract worth three million euros per season with the Serie A runners-up, who open next season at Sampdoria.
Sancho will become the second most expensive English footballer when he joins United, who signed Harry Maguire two years ago from Leicester for £80 million.
Gareth Bale finished with 14 goals in 33 appearances in all competitions for Tottenham after arriving in September.
The pandemic has shaken football. Even one of the world's most valuable teams such as Liverpool is not immune to the impact of empty stadiums draining the business of cash.
In its Global Transfer Market Report, world football's governing body said that the total amount spent on transfer fees of $5.63 billion was down by $1.7 billion on 2019, a fall of nearly a quarter to the lowest cumulative amount since 2016.
Ozil's last match for Arsenal was in March, a week before football was suspended at the outbreak of the coronavirus, so he might not be match-sharp to start immediately for Fenerbahce.
Welbeck was available on a free transfer after leaving Watford earlier in October following their relegation from the Premier League last season.
Mario Gotze joins PSV Eindhoven, Jack Wilshere, Daniel Sturridge among big-name free agents available
Even though the transfer window has closed in Europe's major leagues, free agents remain available to be signed by teams in need of reinforcements.
Llorente, capped five times by Spain, began his career at Real Madrid and moved to Sociedad in 2017. He made 88 appearances in all competitions for the team, scoring eight goals.
Mendy will compete for a starting spot with Kepa Arrizabalaga, who has struggled for form and confidence at Stamford Bridge.