The 26-year-old leaves Barca after 124 first team appearances in the three years since he joined them from Portuguese giants Benfica.
Beer Sheva scored their first goal in the 43rd minute, with Portuguese defender Miguel Vitor heading home from compatriot Josue's accurate pass.
Milan coach Stefano Pioli benched new signing Sandro Tonali and selected Ibrahimovic to lead the attacking line, flanked by Ante Rebic and Samu Castillejo, with Turk Hakan Calhanoglu behind them.
"This is unbelievable, standing here in Paris on the top of the podium. I never thought I would be here," he added.
"FC Barcelona and Inter Milan have reached an agreement for the transfer of the player Arturo Vidal. The Italian club will pay FC Barcelona 1 million euros in variables," read a statement from Barcelona.
Three minutes later, Olivio Da Rosa pulled one back for the Henan side.
Philippe Coutinho also has a lot to prove after his loan spell at Bayern, while questions remain over what style of play Koeman will look to impose.
Nobody will doubt Messi's commitment on the pitch, however, and he will again lead the side this Sunday in an attack which will probably also see Antoine Griezmann, who now has more responsibility following Suarez's departure, and Ansu Fati, who was virtually the only good news to come out of last season.
Last weekend's home defeat to Crystal Palace was a shock to Manchester United fans, immediately prompting fears that last season's progress could be lost after a frustrating summer in the transfer market.
Bale's relationship with Real Madrid coach Zinedine Zidane also deteriorated badly in recent months and he hardly played in the last 11 games of last season as Real claimed the La Liga title.
Even though Hertha was on the front foot, it was the visitor who tripled the lead out of the blue in the 70th minute when Rode had time and space to curl the ball from the edge of the box into the top left corner.