The Manchester United striker headed to LaLiga last month after bosses ruled he could not continue his career at Old Trafford following an investigation into his off-field behaviour.
Greenwood, 22, scored to earn a draw against Celta Vigo last Sunday.
He later said online: “Happy to score my first goal for Getafe.
“Amazing team spirit to come away with a point.”
A source told SunSport he is hoping to stay at the Madrid-based club for the forseeable future, saying: “The players and fans have all given him a welcome he could only have dreamed of.
“He really feared his career was over. Now he’s just so happy and wants to carry on playing and not think too far ahead.”
Greenwood was set to be welcomed back into the fold at United before SunSport exclusively reported the club had made a U-turn following backlash from fans.
The former England international was arrested in January last year following charges of attempted rape, assault and coercive control.
However, all charges were dropped in February by the Crown Prosecution Service.
A spokesperson said at that time: “We have a duty to keep cases under continuous review.
“In this case a combination of the withdrawal of key witnesses and new material that came to light meant there was no longer a realistic prospect of conviction.
“In these circumstances, we are under a duty to stop the case. We have explained our decision to all parties.
“We would always encourage any potential victims to come forward and report to police and we will prosecute wherever our legal test is met.”
