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Right midfielder Flood, 26, joined Boro from Celtic in January 2010, the same day as Barry Robson and Chris Killen completed moves from Parkhead, but his time on Teesside was severely disrupted by serious injuries.
He began impressively and was virtually an ever-present for Gordon Strachan, playing 11 games and scoring once before his season ended prematurely with a knee ligament injury suffered in a 1-0 defeat at Cardiff City in March.
The likeable former Manchester City, Cardiff and Dundee United player worked hard to regain fitness over the summer but dislocated his knee in an accidental collision with Matthew Bates during his comeback game against Ipswich Town at the Riverside on the opening day of this season.
He returned to fitness last month and has made four substitute appearances under Tony Mowbray.
"Willo has been unfortunate in that he hasn't really had a chance to impress while I've been here," said Mowbray. "He has been very unlucky with injuries and his contract has come to an end just when we are looking to reduce costs.
"I'm aware that Willo started very well when he came here and I can see exactly what assets he brings to the team. But I'm looking to put my own stamp on the team and I need to create space in the squad to enable me to bring in my own players."
German defender Haas, 25, joined Boro from Bayern Munich II on transfer deadline day, January 31 this year.
However, he struggled to break into the team, appearing for nine minutes as a sub in the 3-0 home defeat to QPR in February and in just one full game, at right-back in last month's 4-2 win at Hull City.
"We did have an option to give Maxi a further year on his contract, but I have decided to let him move on," said Mowbray.
"I wanted to give Maxi the opportunity to adapt from German football to the English game. The qualities that you get from spending several years with Bayern Munich were there for anyone to see, but ultimately I don't feel he has the right qualities to cope with the physical demands of the Championship.
"Again, he was unfortunate in that he was brought in as a central defender at a time when we were short of centre-backs.
"He wasn't quite ready at that point and, by the time he was, the likes of Matthew Bates, Seb Hines and Stephen McManus had all returned from injury, while Jonathan Grounds was back from his loan with Hibernian."
Stockton-born Davies joined on loan from the Potters in February and began with a Man of the Match display in a 3-2 win at Millwall. He made five starts and one sub appearance but his time on the pitch suffered after a succession of injuries.
"Andrew did very well for us at Millwall but unfortunately has been injured for much of the time since then, which has limited the number of games he has played for us," said Mowbray.
"Like Maxi, he also came in at a time when we were struggling for central defenders. Right now it looks like we're well covered but we thank him and wish him well.
"I wish them all well, whatever they decide to do next, because they are all very good lads who I am sure will do well elsewhere."
Flood is currently still at Rockliffe working on his fitness ahead of next season.
Earlier this week it was announced that goalkeeper Paul Smith has returned to Nottingham Forest after playing a key part in Boro's end-of-season revival, while midfielder Mickael Tavares is going back to parent club Hamburg.
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