The 25-year-old earned himself a reputation as a tenacious striker during his eight years at Celta Vigo, who sold him to the Reds last month for a reported fee of £7m.
Having seen the frontman up close in training, Rodgers believes that the Spaniard will greatly improve his squad.
"When we sat down last year we felt we needed to bring more of that mentality into the group - players with quality but also players with a winning mentality," the Reds boss told the club's official website.
"Iago is a real competitor but he's also got quality as well. We're really looking forward to seeing him in action."
Aspas scored 12 goals in La Liga for Celta last season.