The Blues, who finished third last season, have spent around £80 million in the close season on Luis, striker Diego Costa, Cesc Fabregas and Hajduk Split midfielder Mario Pasalic.
"We finished the market today," Mourinho told BT Sport. "The transfer market closes 31 August and we close on July 19.
"My club did a fantastic job, not just because of what we bought, but because we did it in almost record time.
"The club did fantastic, we knew the targets, we knew the players and the club attacked them and their clubs at a very early stage."
"We got exactly what we need and what we want. The squad is one which I like very much and I look forward to starting the season," the former Real boss said.
The purchase of former Arsenal captain Fabregas was a particular coup but Mourinho said the Spaniard took little convincing and had not been considering a return to the Gunners.
"I spoke with him for 20 minutes. I think he really wanted to come to us," the 51-year-old said.
"Arsenal had an option where they could interfere, but I think he was not open to that. He was very much in our direction, so it was an easy job for me."
Potential starting line-up for Chelsea next season.
- Sports & Recreation
- Cesc Fabregas
- Diego Costa