The Singapore team's plane - Singapore Airlines flight SQ67 - was greeted with a water cannon salute on the tarmac upon its arrival at Changi Airport.
Yip and her fellow Paralympians later emerged in the arrival hall to cheers and applause from fans, their supporters and family members.
"Overwhelmed" was Yip's reply on the warm reception the athletes received.
"Even now, it hasn't really fully sunk in. I'm just happy to return home to celebrate with everybody."
Goh, her close friend and fellow swimmer, added: "Thank you for showing up so early in the morning, we're very glad to be home."
One of the first to arrive to catch a glimpse of the para-athletes was control officer Foo Wah Jong, who took leave from work for the day.
The 50-year-old said: "People don't really treat disability sports that seriously. But I think what they have accomplished is even more amazing than usual athletes. To reach the top in sports is more challenging for them.
"I don't even think that I would come here usually but I want to be here to support them, encourage them because I admire their spirit. I woke up to watch Pin Xiu and I cried when she won."
Manager Christine Chen, 46, made heart-shaped balloons to give to the para-athletes. She said: "It is a small token of thank you to them. When you see them work so hard and never give up, this is the spirit that we all should learn."
Team Singapore won three medals in Rio, where Singapore sent a record 13-strong team, its largest Paralympic contingent so far.
Yip, 24, claimed two golds - in the 50m and 100m backstroke S2 - becoming the first Singaporean to win two titles at a single Paralympics. She also set two world records in the process.
Fellow swimmer Goh, 29, took the bronze in the 100m breaststroke SB4 - her first medal in four Paralympics.
For Yip's father, Mr Chee Khiong, a warm hug rather than any elaborate gesture would suffice when he sees his daughter.
He said: "Just congratulate her and hug her, because I've already seen her in Rio."
Paralympic debutante Norsilawati clocked a new personal best of 1min 49.56sec at the 400m T52 event in Rio. While the 39-year-old is looking forward to reflecting on her maiden Paralympics outing in order to better prepare for future meets, her first order of business is to spend time with her family.
She added: "I'll sleep, then see what I can get my hands on - maybe I'll go for nasi lemak or laksa because I really miss all the local food!"
There will be a press conference with Yip and Goh later on Wednesday afternoon.
A celebratory parade to mark the achievements of the Paralympians will be held on Saturday morning (Sept 24) and start at ActiveSG Sengkang Sports Centre at 57, Anchorvale Road.
The athletes will be driven in a convoy of cars, which will make a pit stop at the National Library along Victoria Street. The convoy will then make its way to VivoCity.
More photos and videos in our live blog here.