Sarginson, 20, was out of contract with the Broncos and joins on a two-year deal with an option for a further year, while the Warriors have paid an undisclosed fee for Clubb, who still had a year left on his Broncos deal.
Clubb, 26, has four caps for England and has signed a four-year deal.
Wigan chairman Ian Lenagan said: “We are delighted to announce that both Dan and Tony will be joining us. Dan is a young player we rate highly and is an excellent prospect.
“Tony is also a player we have admired for some time and has been one of the stand out performers in the London side in recent seasons. “The addition of Dan and Tony will add competition for places within our squad for 2014 onwards and I know both are really excited about the opportunity to play for Wigan Warriors.”
Australian-born Sarginson made his first team debut in 2012, and has made 40 Super League appearances.
He said: “This is a fantastic opportunity for me to join the biggest name in the competition and I am really looking forward to this new challenge in my career. I have had a great time with London and I would like to thank everyone who has played a part in helping me to progress and improve me as a player.”
Clubb has been a regular in the Broncos side since making his debut in 2006, and has scored 47 tries in 150 appearances.
Clubb added: “I want to take this opportunity to thank London for everything they have done for me, I have thoroughly enjoyed my time with them and I have made many great friends. This though is a new exciting chapter of my life signing for Wigan and I couldn’t be happier. I just can’t wait to get started.”