The Tigers confirmed the club-record signing of fellow forward Nikica Jelavic from Everton on Wednesday and less than 24 hours later made a breakthrough in their long-term pursuit of Long.
Jelavic cost an initial £6.5 million rising to £7.5m should Hull stay in the Premier League, and Republic of Ireland international Long would cost them around £7m in a similarly-structured deal.
The 26-year-old has six months remaining on his current Baggies deal, with the club retaining an option of an extra year.
But Albion's sporting director Richard Garlick said the decision to accept Hull's offer came after attempts to pin Long down to a new contract proved unsuccessful.
He told the club's official website: "We began talking to Shane about a new contract last spring and, during the ongoing negotiations, we made him two offers which would have significantly increased his salary.
"However, despite our best endeavours, Shane has declined to sign a new contract.
"Shane effectively only has 18 months left on his deal and with him no closer to accepting our terms and then Hull making an acceptable offer, we felt it was in the club's best interests to accept the bid."
Long was close to joining Steve Bruce's side in September when a private jet was chartered to fly him from the Republic of Ireland's international camp to Hull's training ground.
A move seemed imminent only for West Brom to pull the plug when their own pursuit of Romelu Lukaku fell through.
Long, who is understood to be of interest to other teams in the Premier League including Stoke, now has a decision to make.
- Sports & Recreation
- Premier League
- Nikica Jelavic