Rodriguez has put pen to paper on a five-year contract at the Vitality Stadium, giving Marco Rose an additional forward option alongside Evanilson ahead of Bournemouth's first European campaign.
The Uruguay international arrives on the back of a strong 2025/26 season in La Liga, scoring seven goals and adding five assists across 24 starts and 10 substitute appearances for Elche, with two of those goals coming against Real Madrid and Barcelona.
Born in Palamós, Rodriguez began his youth career at Girona before Real Madrid's La Fábrica academy signed him in 2020. He spent five years in the Spanish capital, making his senior debut under Carlo Ancelotti as an 18-year-old in January 2023 and setting up a goal on his La Liga bow. His first goal for the club followed in his very next league appearance, a dramatic late equaliser in the Madrid derby, rising to head home a Luka Modric corner against Atletico Madrid.
Rodriguez went on to make 10 senior appearances for the 15-time European champions before a loan move to Getafe, and he signed for Elche in the summer of 2025.
Bournemouth's head of football operations, Tiago Pinto, said: "We're really pleased to strengthen our attacking options with such a talented young forward. For someone so young, Alvaro already has a good amount of experience at a very high level and arrives after playing an important role for Elche in La Liga last season.
"We believe he has outstanding pedigree and enormous potential, while also being capable of making an immediate impact as we prepare for an exciting campaign that includes European football. We're looking forward to welcoming him into the group and seeing him continue his development under Marco."
Rodriguez said signing for the Cherries fulfilled a long-standing ambition.
"It feels like a great privilege to be here. I've always wanted to play in the Premier League and now, on my birthday, that dream has become reality. It has been a dream since I was a child. When my agent told me Bournemouth were interested, I couldn't believe it. Everything I've experienced so far has prepared me for this next chapter, and now I want to keep improving and show what I can do."
The signing marks Bournemouth's first of the summer window as they prepare for a season that will include their maiden appearance in European competition.