The Premier League champions completed the signing of the Germany international on Sunday in a deal that could cost them up to €39million.
Roma have already sold Mohamed Salah to Liverpool and Leandro Paredes to Zenit in the close-season, with Francesco Totti retiring, while there has been speculation over the futures of Radja Nainggolan and Kostas Manolas.
Sporting director Monchi insisted this week that they would not allow any more key players to leave the Stadio Olimpico but the former Sevilla man has come in for heavy criticism from supporters for allowing the club to cash in on their top players.
Strootman has wished Rudiger well ahead of his switch to England but he has made it clear that he wants no more departures.
"Good luck to my bro @toniruediger at his new club," he wrote on his official Instagram page. "Im [sic] gonna miss our fights in the training sessions and our discussions in the dressing room. But especially we are gonna miss you on the pitch.
"PS I hope that this will be the last goodbye of this summer."
Amid their high-profile sales, Roma have been active in recruiting new players as they aim to build a squad capable of challenging for the Serie A title next season.
Rick Karsdorp, Bruno Peres, Lorenzo Pellegrini, Juan Jesus, Mario Rui, Hector Moreno, Maxime Gonalons and Federico Fazio have all completed permanent moves to the capital club.