The Blues had been negotiating with Crystal Palace for some time over the 23-year-old striker, however a fee has now been agreed and the player will undergo a medical on Monday.
The Eagles had been holding out for a bid of around £5 million for the international star, but have agreed to accept less as Andy Johnson is travelling in the opposite direction.
Blues manager Steve Bruce did not originally want to let Johnson leave, however the Bedford-born hitman was keen to be reunited with former Blues manager Trevor Francis who is now with Palace.
"Everyone concerned with the transfer has now agreed terms are we are very confident that a deal we be concluded within the next 72 hours," said a club spokesman.
"Clinton Morrison will be travelling up to Birmingham on Sunday night and he will have a medical on Monday.
"Unless there are any unforeseen problems he is expected to sign a four-year contract at some point on Monday, with an option for a further year.
"We would then anticipate holding a press conference on Tuesday."
