An initial search for Mr Barber was launched involving a jet boat, LandSAR search teams, firefighters, ambulance, police officers and family and friends along a 3km stretch of the river north of Double Bridges to a point near Rathkeale College.
The Life Flight helicopter was also called in.
The police national dive squad was called in yesterday to join the search.
Wairarapa acting area commander Scott Miller said the group had been swimming in a water hole when Mr Barber decided to venture to another area near the rapids, which was unsafe.
Mr Miller said friends of Mr Barber had made a "brave attempt" to save the young man when he had initially got into difficulty, but were unable to.
"The force of the current has taken him down under the surface and he's been kept in an area where he can't come back up.
"Unfortunately in this situation it's extremely tragic and we have a death.
"It's extremely traumatic [for the family and friends], they've just seen a friend and a family member brought out of the water, obviously they are very upset but it's good for them to have closure and early closure."
Mr Miller said the swimming area was well-known to the group, who had been regular swimmers there for five years.
"It's a very popular area for swimming; unfortunately with the rain over the past few days the river had risen, the currents through that area have created quite a large rapid ... it's made it far more dangerous to swim.
"The obvious advice here is even if you are experienced in that particular area you've still got to look at the conditions."
Rathkeale College principal Willy Kersten said Mr Barber, a former pupil, was "a very polite, gentle and unassuming young man who worked hard and did everything he possibly could do to achieve".
"He was very much a behind-the-scenes person. He had a lot of good close friends and [he was] a young man who was prepared to be himself," Mr Kersten said.
"I remember clearly a conversation with Jesse and his parents before he left school. He left before most, because he felt he had a plan and school for him was not part of that.
"He was quietly confident and knew what he needed - this is a tragedy."
Mr Barber is the only son of Susan Barber and stepson of John Barber, a farm worker from Kopuaranga. He is described by friends as being a "quiet and polite young man who was very popular and had lots of friends".
Yesterday Wairarapa kaumatua Mike Kawana blessed the area while family and friends consoled each other.
