The duo have followed manager Alex McLeish, who signed a new deal with the Blues earlier this month.
“First and foremost, everything revolves around Alex and once the club came to his agreement on his contract, then we could move forward together,” said Watson.
“Myself and Dave were delighted the owners looked at our contracts.
“I think that was a recognition of the work we are all trying to do here and what we have done as a group over the past couple of years.
“We came back up from the Championship and are trying to get established as a Premier League side, as difficult as that is, and will continue to work hard to achieve that.”