Bebe's arrival comes just weeks after he was snapped up by Portuguese side Vitoria Guimaraes on a free transfer, and Gill was frank about the whirlwind nature of the deal that is reportedly worth in the region of £7 million.
Speaking to MUTV, Gill said: "He's a player we've been following, but he really came on the scene in the last week or so.
"We looked at him, spoke to a number of people about him and then went out and secured the deal.
"It's exciting. He's a potential player, and a lot of Manchester United's focus is about getting players who have the potential and then getting them under the great coaching of Sir Alex [Ferguson], Mick [Phelan], Rene [Meulensteen] and other people.
"He can fulfill that potential with Manchester United and I think it's going to be exciting. Let's hope it works out.''
Gill also suggested that Bebe would not be sent out on loan and would instead be given the chance to settle into life as a Red Devil at Old Trafford.
"He'll join up and be part of the first-team squad this season.
"I think he'll probably stay this year. He has to learn English and integrate into Manchester United, and he's really come from nowhere in a lot of respects."
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