But the Sierra Leone striker will not be the last Bhoy to be loaned out before the window closes at midnight on Thursday.
Manager Neil Lennon has seen the number of players available for selection rise significantly in the past few weeks.
Rami Gershon and Tom Rogic have arrived, while Anthony Stokes, Joe Ledley, Thomas Rogne and Adam Matthews, as well as Kris Commons, have returned after injury.
Kelvin Wilson is once again suspension-free and will come straight back into the side for Sunday's League Cup semi-final against St Mirren.
And James Forrest is finally ready to resume training after being out for all but two games since the end of October.
Paddy McCourt is another who is in the final stages of his rehab from his latest injury.
Fraser Forster's neck problem could still keep him out of the side this weekend, while Efe Ambrose remains on African Cup of Nations duty with Nigeria.
But, Lennon is aware he is going to have a bulging squad for the rest of the season.
And he is currently giving serious thought to allowing some of his players – especially the younger ones – to go out on loan to ensure they get the game time he believes they need.
Lennon anticipates the final week of the transfer window will herald a significant increase in the number of enquiries from managers wishing to take his players on loan.
He had no hesitation in sanctioning the deal which sees Bangura heading back to Sweden.
The striker re-joined AIK – the club who sold him to Celtic for £2.2million 18 months ago – in August, and the Stockholm outfit had hoped to strike a cut-price deal to make the move permanent.
But Celtic are not prepared to take a big hit on the player. And, when Elfsborg came in with a request to take him on loan until December, the Hoops quickly agreed.
Bangura confirmed: "I first learned about the move only on Wednesday, but the clubs had been in contact with each other already."
The 24-year-old has failed to make any impression while with Celtic, and only got his first goal for the top team in last week's friendly with Steaua Bucharest in Spain.
Like keeper Lubos Kamenar, whose loan deal was terminated last week, Bangura was not included in the original squad Celtic registered for the group stage of the Champions League.
So, if Gershon and Rogic are to find their way into 25-man squad for the knock-out rounds to face Juventus – which can include three changes and has to be registered by next Friday – Lennon must still select two names to drop out.