It had been suggested that the signing of the Uruguay international came from the board and was not particularly welcomed by Enrique, who wanted to put his own stamp on the club after replacing Gerardo Martino earlier this summer.
However, Bartomeu has quelled such claims and said that Enrique was delighted to learn of the plans to sign the 27-year-old.
"Luis Suarez was on the table and our new coach Luis Enrique, when he signed, we quickly explained everything and he said 'of course you can bring Luis Suarez to our club. Bring him - he's a fantastic player.' It is incredible to join those three players [Suarez, Messi and Neymar] at the same club. It's something fantastic and something unusual," Bartomeu told Sky Sports News.
"It's rare in the world of football to have three top players plus [Andres] Iniesta, plus [Sergio] Busquets, plus [Gerard] Pique, plus [Javier] Mascherano and the young ones that are coming - it's incredible to have this team."
FIFA have blocked Barcelona from presenting Suarez to the media next week.