Defender Johnson, who joined from Birmingham in 2011, and midfielder Henry, who has played almost 250 times for the club, join Stephen Ward and Jamie O'Hara on the transfer list.
Republic of Ireland international Ward made 37 league starts last season as Wolves suffered relegation while former Tottenham playmaker O'Hara failed to score in his 20 appearances.
"Following the squad's return to pre-season training this morning, head coach Kenny Jackett spoke individually to the four players to inform them of his decision," a club statement said.
"Conversations had already taken place with the players' agents throughout the close season as Wolves prepare for the League One campaign."
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