Christophe Galtier's side have moved quickly in the transfer market in the wake of sealing their 11th Ligue 1 title, but the Parisiens suffered more disappointment in Europe last term.
PSG are still waiting for their maiden Champions League crown after losing to Bayern Munich in the last 16 of the 2022-23 tournament, and a mass exodus of players is thought to be on the cards.
Lionel Messi and Sergio Ramos have already announced their exits, while Leandro Paredes, Georginio Wijnaldum, Layvin Kurzawa and Julian Draxler could also be on the way out in the coming weeks.
The Ligue 1 champions identified Asensio and Sporting Lisbon's Ugarte as their two primary targets for the summer window, and both transfers are seemingly set to be made official in the coming hours.
According to Fabrizio Romano, the duo have now penned their contracts at the Parc des Princes after completing their medicals on Monday, and announcements are imminent.
PSG are believed to have held a long-standing interest in Sporting midfielder Ugarte, but Chelsea appeared to have moved to the head of the queue for his signature over the weekend.
However, in a surprising turn of events, Chelsea pulled out of the race to sign the Uruguay international, having apparently baulked at the financial demands of the deal.
As a result, PSG swooped in and triggered Ugarte's €60m (£51.7m) release clause, and the 22-year-old is believed to have put pen to paper on a five-year contract in Paris.
Ugarte departs Sporting having scored one goal and set up three more in 85 appearances for Ruben Amorim's side in all tournaments, including one assist from 47 matches in the 2022-23 campaign.
Meanwhile, Real Madrid recently confirmed that Asensio would end his successful eight-year stint at the Bernabeu when his contract expires at the end of the season.
The 27-year-old was believed to have been on the radar of several Premier League teams, but he opted to join PSG and will commit the next four years of his career to the Ligue 1 champions.
Asensio leaves Real Madrid having won three Champions Leagues and three La Liga titles since 2015, scoring 61 goals and providing 32 assists in 286 appearances.
The Spaniard contributed 12 goals and eight assists from 51 appearances in the 2022-23 campaign, but he started just 15 La Liga games amid competition from Vinicius Junior, Rodrygo and Federico Valverde.