Portuguese defender Bruno Alves' contract with Rangers has been terminated by mutual consent.
The centre-back, 36, has been allowed to leave after just one season at Ibrox, when he played 28 matches.
However, manager Steven Gerrard has denied that full-back Lee Wallace is on the way out, despite being left out of Rangers' initial Europa League squad.
"Me and Lee are fine," said Gerrard. "He's got an issue with the club and he's currently injured."
- Lee Wallace backs new Rangers captain James Tavernier
- Rangers sign African pair Lassana Coulibaly and Sadiq Umar
Alves arrived at Ibrox last summer from Serie A side Cagliari and still had 12 months left on his contract, but the summer arrivals of Connor Goldson and Nikola Katic had pushed him down the pecking order.
"Both parties are really happy and we both move on," Gerrard said. "He's about to be unveiled at Parma and we wish him all the best."
Gerrard has brought in nine players ahead of his first competitive game in charge of the club - Thursday's Europa League first qualifying round tie at Ibrox with Macedonian side FK Shkupi.
African pair Lassana Coulibaly and Sadiq Umar followed veteran goalkeeper Allan McGregor, full-back Jon Flanagan, centre-backs Goldson and Katic, midfielders Scott Arfield and Ovie Ejaria, and winger Jamie Murphy - on a permanent deal after a successful loan spell - in joining Rangers.
'Coulibaly is a destroyer-type'
Although the former Liverpool captain has not ruled out more new faces, he says he is close to completing his squad rebuilding.
"We're nearly there," he said. "There is no number on new signings to arrive; we will be ready when we decide we have a squad to challenge domestically and in Europe.
"Good players are on the same wavelength, and good players gel pretty quick.
"Bruno Alves' contract has been terminated mutually. It doesn't open the door for me to go and sign more players. The board of directors have been very supportive. I knew we needed to make changes and they've backed me so far.
"[Umar] is a talent, a player with huge potential. He's looking for a stage to take his career to the next level. He's one of many boys who are at top clubs around the world and suffering, not playing.
"The likes of Rangers can grab these boys and give them the stage to perform on.
"Coulibaly is a destroyer-type midfielder, he is very different to what he have here. I have watched him numerous times and he breaks play up and keeps it simple. He will add a bit of power in the engine room for us."