In just over eight seasons at the Molineux, Dougan made 320 first team appearances for Wolves netting over 120 goals.
Shackell has signed a four-year contract with the Molineux outfit.
The two sides are due to meet at Molineux after the international break on 16 October.
His widow Samantha and their children Rio and Jaden joined the teams before the match at Molineux.
BBC: Clubs pay tribute to Dean Richards at Wolves-Spurs game
The Frenchman, who has an option on a fifth year, completed his move to Molineux following the Tigers' relegation from the Premier League.
From Chasetown to Accrington, and Molineux to the Millennium, we've put our heart and soul into the FA Cup.
He had joined Wolves from Dundee in 2011 but was unable to break through to the first team at Molineux.
Henry has been no stranger to controversy this season, having been involved in a series of physical exchanges with Newcastle midfielder Joey Barton when the teams met at Molineux in August.
Hunt follows defender Steven Mouyokolo from Hull to Wolves to become the fifth summer arrival at Molineux.
But in front of a sold-out Molineux, Wolves held on for the three points and a place in the cash-rich Premier League.
The Wolves boss also said he is in no rush to make a decision over Bobo Balde, 33, as the former Celtic defender has been on trial at Molineux.
The 22-year-old midfielder signed a three year deal at Molineux earlier this month, after deciding to leave Southampton for a seven figure fee.
Against the backdrop of Pompey's off-field financial problems, Hassan Yebda's goal clinched a 1-0 victory over Wolves at Molineux, ending a run of seven straight Premier League defeats since the start of the season.
Watching England coach Fabio Capello may have chosen Molineux more for its proximity to Villa Park, where he had taken in the lunchtime kick-off, than the huge number of national team candidates on parade.
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