Los Blancos have signed Aurelien Tchouameni in a big-money deal from Monaco, while Antonio Rudiger has made the move to Bernabeu on a free transfer from Chelsea.
Real Madrid continue to be linked with a number of other players, with the club still thought to be keen on a new attacker, having missed out on a deal for Kylian Mbappe earlier this summer.
However, Ancelotti has said that the La Liga champions are "fine" with their squad for the new campaign.
"I can tell you we won't sign anyone. We're fine as it is," Ancelotti told reporters on Thursday, with Real Madrid preparing for pre-season games against Barcelona, Club America and Juventus.
The Real Madrid manager also hailed the signings of Tchouameni and Rudiger, with the Italian confident that both players "will bring a lot of quality to the squad".
"Tchouameni and Rudiger will bring a lot of quality to the squad. Rudiger is a great centre-back who can play in different positions, while Tchouameni is the same as a midfielder," Ancelotti added.
"He is younger but is already playing for the France national team. Competition in the squad is the key to success. They both only arrived today. Of course they'll need some time to adapt, but not too much since they have so much quality."
Ancelotti is also targeting another successful season in 2022-23, having led the team to a La Liga and Champions League double last term.
"Winning gives me a lot of happiness so I want to keep this moment of happiness. We'd like to repeat this season what we did last season. We are looking to adapt new players into our philosophy. We have room to improve and do better compared to last season. We have more confident and knowledge," he said.
Ancelotti has also addressed suggestions that Eden Hazard could be used as a centre-forward during stages of the 2022-23 campaign.
Karim Benzema will again be the club's number one striker next season, but Luka Jovic has moved on to Fiorentina, while Mariano Diaz and Borja Mayoral could both depart before the end of the window.
"We have a lot of options for that position. Benzema is the top one. But, we have to understand it'll be a strange season with the World Cup in the middle. Given the quality Eden has, it could be good for us to have him there," the Italian added.
Ancelotti is also looking forward to the Clasico against Barcelona in Las Vegas: "It's never a friendly against Barcelona. The fact we face them early in the season is good too. We'll both want to win this game here and put on a show, as Real Madrid vs Barcelona always is."
Real Madrid will open their 2022-23 La Liga season against Almeria on August 14.