The 6ft 5in midfielder, who clinched his £700,000 move from Israeli side FC Ashdod on Friday, joins his former team-mate Ambrose and countryman Beram Kayal at Celtic; all three players share the same agent. And Ambrose feels the 21-year-old, a stand-out for Israel as they hosted this summer's European Under-21 Championships, has the attributes and work rate to get to the very top.
"For me he is a great player," said Ambrose. "In his stature and the way he plays he reminds me of [Sergio] Busquets at Barcelona - there are similarities in the way they run and pass. I've played alongside him at Ashdod and he is a young boy who really wants to succeed. He always does extra training to improve himself. He has qualities that will really make him do well here.
"I'm not sure he is a direct replacement for Victor [Wanyama] because they play two different roles," added the Nigerian. "Nir is a kind of supporting midfielder and when we played together I was playing more defensively alongside him.
"But he is a very good player, he is young and it's great that we can make him part of a team that is going to be in the Champions League. I experienced that when I arrived here a year ago, it's a great thing to step into."
"We have spoken a lot about the club. He asked me what it is like here and I've told him it is terrific for a young player - if you want to step up your game this is the right place to come. Being at Celtic has made me a better player and I have achieved things I never had before. There are plenty of challenges, a lot of trophies to win.
"It is going to feel like home for Nir because I'm here and Beram is too. He will have friends he can rely on. I talked to him before he left Israel and he was asking about the weather and everything. I told him it's not too bad!"
With Biton's arrival only the first name in a late transfer spree, Ambrose feels Celtic can surpass last season's achievement of making the last 16 - even though the group pits them against Barcelona, AC Milan and Ajax. "After what we did last season nobody is going to look on Celtic as underdogs," said Ambrose.
"We are going to have to raise our game again to try to match these teams. The new signings will help us and we need them because we have a lot of games to play.
"There will be times when we will be tired and we will need the new players to give us that freshness. It was a great achievement to make it to the last 16 but you always want to improve. The challenge is there for us to step up and try to make it to the quarter-finals."