The 24-year-old left the Ireland camp on Monday to complete a move from Reading to West Bromwich ahead of Wednesday night's friendly against Croatia in Dublin.
The fee was a transfer record for the Midlands club, surpassing the ?4.7m they paid for Spanish midfielder Borja Valero three years ago.
On the move: West Brom will smash their transfer record to sign Long
He becomes the sixth Ireland player who featured against Macedonia in June to move on during the close season.
And his move ends months of speculation for Long who was linked with Newcastle United, Everton, Celtic, Leicester City and West Ham United following Reading's failure to reach the Premier League in last season's Championship play-off final.
Trapattoni, who will play Long, his former Reading and Cork partner Kevin Doyle, new Baggies team-mate Simon Cox and Ireland captain Robbie Keane in tomorrow's friendly at home to Croatia, said the 24-year-old now had the platform to go on and improve with one of the best coaches in the business.
West Bromwich boss Roy Hodgson, an old friend of Trapattoni's who recommended Simon Cox for the Irish squad, sought the Italian's opinion on Long before making his move.
And Trapattoni said: 'He is young and, in every game, he can learn more. He will be playing regularly against stronger opponents and he can only learn and improve more from that.
'He has good qualities. He jumps very well, he is fast, he has no fear, he can shoot with his left or right foot and head the ball because he jumps very well and he defends the ball very well.
Long wait is over: Striker Shane has been linked with several clubs this summer
'He has improved already, but he can improve more and he needs to improve in the other areas of the game.
'It's very important to be strong and, also, he needs to understand the game better to help his colleagues, and when to make sure he can make his runs because he is very fast which is a very important quality in the modern game.
'It's important that when you are busy, I can help you. He is young and needs to understand this and, usually, the young need experience. He will get this now.'
With Keane and Doyle likely to start against the Croatians at the Aviva Stadium on Wednesday night, the Cox/Long partnership is likely to get its first airing for the second half tomorrow night.
Trapattoni is certainly pleased the young pair, who had very different roles in the win in Macedonia in June, will now have time to develop together at their club.
He added: 'I told Roy it is a good mix because one is fast, and the other Cox, plays with a bit more experience. They could be a good combination.
Progress: Simon Cox developed his game for West Bromwich Albion last season
'When you see Cox, he looks before he receives the ball, which is important, and he knows his position. There are the other players who have different habits and they wait for the ball because they are fast. In the Premier League, Shane can learn this way of playing.'
Trapattoni has decided he will use all four strikers tomorrow night but his squad is now down to 16 outfield players following withdrawals through injuries after the English Football League started at the weekend, plus the latest round of pre-season matches for top flight sides.
Among the absentees are James McCarthy, Marc Wilson and Jon Walters, who all controversially pulled out of the qualifier in Macedonia and the three end of season friendlies.
Eyebrows may have been raised, particularly over Wigan star McCarthy's absence, but Trapattoni was more relaxed about his lot on Monday, happy that lessons have been learned by players and FAI coaches and staff since the messy issues of three months ago.
Trapattoni added: 'It is not my habit to cry about injuries. We have enough players to play important friendly games against Croatia. This is a good little test for me and for us before the important games against Slovakia and Russia.
Out: Wigan midfielder James McCarthy will miss the Ireland game due to injury
'McCarthy has been in touch with me and he said he wanted to come but he had the scan and he needs two or three days to recover so I said it is impossible for him to play in that time for us.
'I am content. We have grown and I think the players understand what we need from them. When the players didn't make contact before I said `never again'. We need to be clear, sincere and honest.
'Our players shouldn't wait before answering us. They should make contact right away and we have progressed in this situation. They all answered to me immediately, to our secretary and to our doctor and said whether they were available for us.
'In fact, also, with two injuries to Walters and Wilson, they were here so we could look at them. They came, we tested the injury and they went back. I repeat, I always defend our players and I expect the same respect from them.'
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