The club announced Yoshida had put pen to paper on a new three-year contract just a few days after completing the signing of Netherlands international Hoedt from Lazio for £15 million.
The 23-year-old became the second central defender to sign for the Saints during the summer transfer window, following on from Jan Bednarek's £5m arrival.
The duo were thought to be have been signed in preparation for Virgil van Dijk's departure but with Southampton refusing to sell the Dutchman, boss Mauricio Pellegrino now has plenty of defensive options at his disposal.
Jack Stephens and Yoshida have been Pellegrino's preferred choice at centre-half thus far this season, but with van Dijk, Hoedt, Bednarek and Florin Gardos all hopeful of game-time, Yoshida faces a battle to keep his current spot.
The Japan international is relaxed about the situation and says the competition for places makes the Southampton squad stronger.
"I have no reason to leave the club," Yoshida told the Daily Echo. "I have been here for better or for worse in the last five years and still I have to fight for my position because two days before I signed my new contract they got another centre-back.
"At this level in the Premier League everywhere you have the competition between the players, especially between Southampton centre-backs competition is very high.
"But the competition makes us very strong. I have learned the last couple of years so I really welcome this kind of competitiveness between the players.
"I want to show my ability and character to the fans, the club and the manager."