The 28-year-old central midfielder was appointed the West Ham captain on a permanent basis on Monday prior to the home match against Newcastle United in the Premier League.
Noble started the encounter at the Boleyn Ground and played for the entire 90 minutes, as the Hammers registered a 2-0 win.
Following the match, former Arsenal striker Wright congratulated Noble on getting the West Ham captaincy on Twitter.
Noble has been at West Ham his entire professional career and is an important part of the club’s future.
It made perfect sense for the Hammers chiefs to make the former England Under-21 international the first-team captain following the departure of attacking midfielder Kevin Nolan in the summer transfer window.
West Ham are fifth in the Premier League table at the moment with nine points from five matches.