The captaincy has been bestowed upon the 23-year-old by Gareth Southgate for the Three Lions' World Cup qualifier against Scotland on Saturday.
And Spurs captain Lloris was full of praise for his club's star man, having watched him step into the role in the goalkeeper's absence on occasion.
"Obviously his destiny is to be one of the best strikers for England and hopefully he will get success with the armband."
Lloris said he believes his team-mate's traits on the pitch for Tottenham will translate to the international stage, where Kane has already amassed 17 caps.
"When he's on the pitch, he's always positive, he is working hard for the team," Lloris said.
"He is very involved in the squad and I'm sure he will do it in the same way with England national team.
"I think the responsibility is not only on his shoulders. It's about leaders.
"They have a lot of young players but with the capacity to be leaders and hopefully they will get success under Harry."