The 31-year-old Swansea defender has moved to Pittodrie on loan until the end of the season.
He goes straight into the Reds squad for the Scottish Premiership clash at Kilmarnock on Sunday but has already got one eye on next month's League Cup semi-final with St Johnstone.
Asked what he wanted to take out of his spell with Derek McInnes' side, the former Manchester United youth told RedTV: "A medal, first and foremost. That will mean the club has done well and got into Europe.
"The manager spoke about that to me and it would be a big thing for any club to win a major trophy."
Aberdeen's 2-1 win over Dundee United on New Year's Day cemented their position in third place and Tate said the prospect of helping the club win its first trophy in 18 years was a major factor in his decision to move north.
"The manager told me they were going well in the league, had a cup semi-final to look forward to and that there was a good chance for them to get into Europe," he said. "He sold me on the way that he wants to play good football, so that was it really, nothing else had to be said.
"Aberdeen is pretty similar to Swansea in that it is the only club in the city, so you can see the potential there, as it is a big enough city. I'm sure if the club improves further on how it did last year, the attendances will get even bigger.
"Everybody knows about the time when Sir Alex Ferguson was here and them winning the European cups so you are aware of what the club has done in the past.
"But it's a new challenge for me and that is one of the reasons why I have come up here. We play Kilmarnock on Sunday but I wouldn't even know where Kilmarnock is? Is it a city?
"I've played in every league in England and was happy with how things have gone down there. This is a different challenge and one that I'm ready for. I've never played up in Scotland and if you spend all your life where you are comfortable, you won't achieve much."
Tate has played more than 280 games for the Swans and has been on loan at Championship clubs Leeds and Yeovil this season.
The centre-back joins a back four which will be missing the injured Andrew Considine and Clark Robertson for the next few weeks.
Reading defender Michael Hector is also due to return south when his loan spell ends after Sunday's meeting with Killie - although he could return later this month if Royals boss Nigel Adkins' injury concerns ease.
However, McInnes admitted he could not risk ending up without cover, saying: "I've made no secret of the fact that, even if Michael does come back, we are pretty short in terms of cover in that department, and I'm delighted to bring in someone with Alan's experience.
"We can't sit about and wait on Reading to make a decision so when the chance to bring someone of Alan's quality here, we tried to move on it quickly.
"While Alan is predominantly a centre back, he can also play at full back if required, and he'll go straight into the squad for Sunday."
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