The former England fly-half came out of retirement at the end of last year to join Premiership side Newcastle on a three-month contract.
The 35-year-old, who started his professional rugby career with Leicester in 1998, has since played for five other European clubs, which include 83 caps for Worcester and 36 for Brive.
Goode, who also had a brief stint in South Africa with the Sharks in 2010, has made six appearances since joining the Kingston Park club.
The contract comes to an end after the Wasps fixture which takes place next weekend.
Although shortlived, the fly-half has had a good stay with the Falcons.
“I have enjoyed my time with Newcastle Falcons and would like to thank Dean, the entire staff and the Falcons’ supporters for the welcome I have received,” Goode said to the Newcastle website.
“I have been able to play some part in delivering positive results for the club, and I will take fond memories from my time in the North East.”
The Newcastle boss Dean Richards is grateful for the void that Goode filled following the injury to Mike Delany.
“Andy answered our call when we had lost Mike Delany to a long-term knee injury, and he has done a fantastic job for us during his four starts and two bench appearances,” said Richards.
“The experience and control that he was able to add to our play was valuable in helping secure victories over Leicester Tigers, Northampton Saints and Harlequins, and our young players have been able to learn from everything Andy brings to the game.”
“He will be fondly remembered by us and our supporters for the contribution he has made during his three months with us, but with Mike and Tom Catterick both back fit now it is the right time to thank Andy for his efforts and wish him all the best for the future.”
The former Saracens number ten has emphasised the importance of next Sunday’s home match against Wasps.
“But the job isn’t done yet. There is still one last game before my commitment to the club ends, and that is a huge home tie next Sunday against Wasps.
“I would love to be able to sign off by playing a part in one last victory during my time with the Falcons, and naturally wish them all the best for what remains of the season.”