Jack Simpson says he is up for the challenge of breaking into Steven Gerrard's rampant Rangers team.
Both will now aim to play a part in the Light Blues' title procession as the champions-elect close in on their first league crown in a decade. But the task appears to be a little tougher for Simpson as he attempts to force his way into a back four that has shipped just seven league goals this season.
However, the centre-back – who like Wright has agreed a four-and-a-half year deal – told the Rangers website: "I am super excited to be here.
"This is a massive club and I am honoured to be a part of it. I can't wait to pull on the shirt, and play in front of the fans and at the stadium.
"It is obvious how big this club is – it's one of the most successful clubs in world football so I am delighted to be here.
"It is going to be a huge challenge to keep up with everything that has happened and to keep pushing myself to stay at the standards that are expected here.
"That is very important to me and I am excited to try and do that."
Rangers manager Steven Gerrard added: "We are delighted to have Jack here. We have been aware of him for some time and excited to finally have him.
"Clearly it's a bonus to have him here now earlier than initially planned. His presence makes us stronger and we are all looking forward to working with him."
Wright's move also went through six months early after Aberdeen were given a £150,000 discount on Ross McCrorie's Pittodrie switch, the PA news agency understands.
Gers agreed to slash the £350,000 fee they had agreed with the Dons to make McCrorie's loan move permanent in the summer and the Scotland Under-21 captain will now become an Aberdeen player outright.
Wright said: "I'm delighted to be here at this massive club and can't wait to run out at Ibrox for my debut, and then hopefully in front of a full house in the not-too-distant future.
"It is a real privilege to have the opportunity to work under a manager like Steven Gerrard and speaking to him and Ross Wilson, I am really impressed with how everyone at the club all have the same aims and ambitions.
"I cannot wait to meet my new team-mates and get started as a Rangers player."
Gerrard added: "We are delighted to have Jack here. We have been aware of him for some time and excited to finally have him.
"Clearly it's a bonus to have him here now earlier than initially planned. His presence makes us stronger and we are all looking forward to working with him.
"It's also very pleasing to have Scott for the rest of this season. This will give him the opportunity to gain some valuable game time in a blue shirt for the rest of the season.
"Scott is a player that I have admired and I believe that we can utilise his skill set within our system. He will train with his new team-mates tomorrow."
McCrorie has now officially cut ties with Ibrox.
He said: "I'm really pleased to officially be an Aberdeen player. I'm looking forward to continuing my development and being part of this exciting squad.
"We've still got a lot to play for this season, with some big games in the coming weeks, so there is much to look forward to."