The 25-year-old goalkeeper has agreed a five-year contract and will compete for the number one jersey with Álvaro Fernández and Germán Parreño.
Román had a strong season for Mallorca, though it was not enough to prevent his side's relegation.
His performances led to a call-up to Spain's senior squad under head coach Luis de la Fuente for the friendly against Iraq at Riazor.
Román moved to Mallorca two years ago after playing for Real Oviedo in the Segunda División, and has been one of the players to develop and stand out most over the past two seasons.
The fee has not been officially disclosed, but sources close to Mallorca said it is in the region of €5 million.
Deportivo's move followed Mallorca's relegation to Segunda División, which reduced Román's release clause from around €12 million to €9 million, according to reports carried by Galicia Press.
Transfer market specialist Matteo Moretto reported that Deportivo paid the €9 million clause in full at LaLiga's offices, according to eldesmarque.
Infobae confirmed the club executed the release clause and handed Román a contract running for the next five seasons.
Deportivo sporting director Fernando Soriano had tracked Román since working with him at UD Ibiza, where the goalkeeper played for San Rafael and Penya Deportiva before joining Mallorca's B team in 2020, Cope reported.
According to Radio Coruña, Román turned down higher financial offers from clubs in Italy and Turkey to join the Galician project, while Real Sociedad and Atlético Madrid had also monitored his situation in Spain.
Before his move to Mallorca, Román spent the 2023-24 season with Real Oviedo in the second tier, playing 42 matches and keeping 14 clean sheets, Infobae reported.
He went on to make 40 appearances in LaLiga across his two seasons at Mallorca, according to the same report.
Román's arrival is expected to challenge Álvaro Ferllo, who had been first choice at Riazor for much of Deportivo's promotion campaign, Galicia Press reported.
The club had also considered Diego Conde of Villarreal and Julen Agirrezabala, on loan at Valencia from Athletic Bilbao, before turning to Román.