He is expecting to fit in quickly.
"I'm glad I'm joining the rest of the team," he said.
"They've been working hard since the beginning of July and in Zlatibor doing their strenuous preparations, so it is my pleasure that I am joining the preparations and am ready to start working with the rest of the team.
"I worked individually in Bar (Montenegro) so believe that there will be no problem getting used to the system of work in Zlatibor and continue preparations for the European Championship, which we all await with great impatience."
Vucevic doesn't believe that his late arrival is cause for concern.
"Most teams' preparations began at the end of July or are beginning right now, so I think we have enough time to put everything in place," he said.
"We have enough time to practice and will have a sufficient number of friendly games and I'm sure we will be ready at the start of the tournament.
Montenegro are still wait for Nikola Pekovic, although he is expected to arrive 5 August.
"I think Pekovic and I will not be a problem to fit the requirements of (coach Luka) Pavicevic and his coaching staff," Vucinic said.
"The atmosphere in the team is great and I believe that all this will give the result of what everybody wishes."
If they finish in the top six, qualification for the Basketball World Cup will be secure.
Should Spain - the hosts of the 2014 FIBA Basketball World Cup - finish in the first six, then a top-seven spot at the EuroBasket would be good enough for Montenegro to advance to next year's showcase event.