The Clydesdale Bank Premier League champions have the chance of finishing the campaign on a high when they take on Hibernian in the William Hill Scottish Cup final later this month.
However, Ambrose, who joined Celtic from Israeli Premier League club FC Ashdod last summer, has already experienced cup glory with Nigeria in February when he was part of the side which won the African Nations Cup with a 1-0 win over Burkina Faso in Johannesburg.
Ahead of the trip to Ross County in the SPL tomorrow he reflected on his first season with the Hoops, which also brought a run to the last-16 of the Champions League.
"It is my first time playing in Europe and coming to Celtic was a great move for me," said the 24-year-old Parkhead stopper.
"My aim is to keep playing and keep improving and do better than what I am doing now.
"It is going to be a great season but I cannot achieve this on my own.
"I have to thank everybody because without them I would not be here or have won the Nations Cup.
"The fans, the players and the manager really made me welcome and made me a better player.
"Right now the most important thing is the cup final, which I know is going to be a great achievement for us at Celtic because winning the double is something they have not done for a while."