Having failed to get what they wanted out of Fiorentina loanee Sofyan Amrabat during 2023-24, United have been in the market for a new centre-midfielder all summer.
That particularly became necessary once the green light was given for Scott McTominay to make the switch to Napoli, Ten Hag admitting that he had mixed feelings over the exit of the Scotland international.
However, by that point, negotiations were well underway for Paris Saint-Germain's Ugarte, who had been made available after just a season at Parc des Princes.
Late on deadline day, United confirmed that they had agreed to sign the Uruguay international for a fee that could reach almost £51m if all add-ons are met.
Ten Hag anticipating "controlled aggression"
Ugarte is not in a position to make his debut for United against Liverpool on Sunday having not been signed before the Friday midday deadline.
Given what Ten Hag said in a pre-game interview with Sky Sports, the Dutchman is disappointed that he cannot use the 23-year-old against one of the club's fierce rivals.
Ten Hag said: "I think he is a very good fit to Manchester United. I think he is a very good fit to this team because this team needs that controlled aggression.
"He is a very brave player, so we will be really happy. I am sure he will really contribute to our success."
Will Ugarte go straight into the team?
Although Casemiro has started alongside Kobbie Mainoo for the first two Premier League fixtures, it would come as a surprise if Ugarte did not feature against Southampton on September 14.
That is despite Ugarte not playing any competitive football since the third-place playoff against Canada in the Copa America on July 14.
However, he will likely be used in Uruguay's upcoming three matches across the international break with his national team facing Guatemala, Paraguay and Venezuela.
With United playing in the early kickoff on Premier League matchday four, Ugarte may only participate in one training session before the game at St Mary's.