The 26-year-old will subsequently complete a permanent transfer to the Championship side when the transfer window reopens.
Doidge is set to move for an undisclosed fee which Forest Green chairman Dale Vince has described as a club-record seven-figure amount.
"I'm really grateful to Christian - for all his time here and his incredible loyalty," Vince told the FGR website.
"Last January he declared he was going to stay and help us beat the drop from League Two - which he did. That felt exceptional to me at the time - you know who your true friends are when the chips are down.
"Letting Christian go today is in part about repaying that loyalty - it's a great opportunity for him, and one he's earned. We are disappointed to be losing him but at the same time it's hard not to be excited for his future.
"In departing, Christian has set two club records - our top all-time goalscorer, and a transfer fee in seven figures."
Doidge scored 49 goals in 87 league games for Forest Green after signing from Dagenham & Redbridge.