Shanghai, who are ninth in the Chinese Super League, fired Frenchman Tigana in April after a poor start to the season, replacing him with interim coach Jean-Florent Ibenge.
"I hope that Shanghai Shenhua will be the best. There is perhaps no one word to describe my hopes," Batista, with the help of a translator, told a news conference.
"Perhaps the current situation of the team is not too ideal, but overall I think we will do something important and have a good result.
"This project is a challenge for me so I will do my best to win the league. But it is also a gamble. I believe if we do our best, we can do it," the 49-year-old added.
Batista, who said he wanted to sign Chelsea striker Didier Drogba, coached Argentina to Olympic gold at the 2008 Beijing Games before replacing Diego Maradona as national coach.
He was sacked after only a year following Argentina's failure to end an 18-year wait for a major title at the 2011 Copa America.
French striker Nicolas Anelka, who joined Shanghai from Chelsea in January and was player-coach after Tigana left, said he was unhappy at being kept in the dark about the appointment.
But former Argentina midfielder Batista, who has the option of a one-year contract extension, said Anelka was a key part of the club's future and they already got on well together.
"First of all, I have a good relationship with Anelka. We have had good communication during the past few days. So we have been talking and, as a player, Anelka plays a very important role," Batista said.
"...he can bring a level of experience to help this team. Also, he has been very welcoming of my arrival..."
Shanghai have been strongly linked with a move for Anelka's former Chelsea team mate Drogba, who has announced that he is leaving the Champions League winners at the end of June.
Batista, who will take charge for the first time in a friendly on Sunday against South African club Moroka Swallows, fuelled the speculation surrounding the Ivorian striker.
"My initial thought is to bring Drogba to the club. He is a very good player and we will welcome him here... I very much hope that Drogba can join us," he said.
Chinese clubs have splashed out on big name foreign managers and players to try to raise the profile of domestic soccer.
League leaders Guangzhou Evergrande this month appointed Italy's former World Cup-winning coach Marcello Lippi after sacking South Korean Lee Jang-soo.