The younger brother of Toon striker Shola has found his first-team opportunities at St James' Park limited and will join up with their North East rivals for the rest of the season
The 20-year-old, younger brother of striker Shola, can play up front or on the wing and has made 14 senior appearances in all competitions for the Magpies this season, eight of them as a substitute.
Newcastle boss Alan Pardew revealed that the club were in talks with their North East rivals regarding a possible temporary switch for Ameobi after the 4-2 victory over Southampton on Sunday.
"We are going to talk to Middlesbrough," he told reporters. "I would like to help Middlesbrough out if they want him, and hopefully we can conclude that."
Promotion-seeking Middlesbrough are currently seventh in the Championship and one point off a position in the play-offs with 12 games remaining.
Ameobi will miss the FA Cup fifth-round clash against Chelsea as he is cup-tied but could make his debut against league leaders Cardiff on Saturday.