Sevilla completed the signing of the 22-year-old from Swedish league leaders IK Sirius this week, in a deal reported at an initial €6.5 million with a further €2.5 million in possible add-ons.
Ure has signed a five-year contract running to 2031 and will wear the number nine shirt for Luis García Plaza's side, who face Rayo Vallecano this weekend.
"I found out about Sevilla's interest maybe three weeks ago. My reaction was, of course, a lot of emotions. When I found out, I just thought about coming here and playing for Sevilla," Ure said.
"As I said, it's a very big club in Spain, but also in Europe, and the chance to come here and play was something I wanted very much."
The forward, who moved to Sirius from Anderlecht's youth academy having previously come through Rangers, said reaching one of Europe's top five leagues had been the plan all along.
"When I went to Sirius, in Sweden, the plan was to reach one of the big five leagues. But when I found out about Sevilla's interest, it didn't take me long to think it over, because I knew I wanted to be here. It's a huge club."
Ure has scored 15 league goals in Sweden this season, part of a run that has taken Sirius clear at the top of the Allsvenskan table, and says confidence has been central to his recent form.
"I think this season I've gained confidence and more belief that when I get a chance, I can take it. Scoring goals depends on staying calm, slowing everything down and really just thinking about yourself and the ball. This season I've been doing that really well and I've been very calm mentally in these situations. I hope I can keep doing that."
He is eager to make an immediate impact at the Sánchez-Pizjuán.
"I played last week, so I'm ready to play and I'm really excited to do it," he said, before describing what supporters could expect from his style. "I think my biggest strength is scoring goals. I don't care how the ball goes in, they all count and my main priority when I go on the pitch is to score goals. I have other qualities too, of course, but that one, for me, is one of the best. I have qualities that make me difficult to defend against, because I can drop deep, link play and hold the ball, but I can also be a technical player capable of creating chances for others."
A conversation with head coach García Plaza before the move helped seal his decision.
"I spoke to the coach last week and it was a good phone call. I have a lot of respect for everyone, and when I spoke to him, he explained how he likes to play and how I can be effective for his team. After that conversation I felt, without doubt, that I wanted to be part of his team."
Ure, who has represented Scotland up to Under-21 level, signed off with a message to his new supporters.
"Thank you for the welcome. I'm really excited to meet you all, and you're going to have someone who will give everything for this club."