Birmingham had already broken the League One incoming transfer record twice in this transfer window before completing the deal to sign Stansfield.
Sky Sports News understands it is an initial £15m, but sources in Birmingham say it is less.
Christoph Klarer and Willum Thor Willumsson were both signed for fees in the region of £3.5m, but the Stansfield transfer smashes both of those numbers.
He scored 13 goals in 37 appearances during his spell at St Andrew’s, which saw him recognised with the club’s player-of-the-season award.
Stansfield scored against Birmingham in midweek in Fulham’s 2-0 win in the Carabao Cup second round.
Birmingham City have signed Celtic midfielder Tomoki Iwata and Rangers winger Scott Wright, both for undisclosed fees.
The pair have signed three-year contracts at St Andrew’s.
Iwata, 27, made 42 appearances for Celtic and won two Scottish Premiership titles, two Scottish Cups and one Scottish Cup at Celtic Park.
Wright, also 27, won the Scottish Premiership, Scottish Cup and League Cup during his three years at Ibrox and started in the Europa League final defeat by Eintracht Frankfurt two years ago.
He is the second player Blues have signed from Rangers this week following the arrival of former Preston and Liverpool centre-half Ben Davies.
Meanwhile winger Koji Miyoshi, 27, has joined German side VfL Bochum for an undisclosed fee.
