It was the first time Mr Thompson had seen his son since April 2008, when the boy was taken to Europe by his mother, Melinda Stratton.
The overjoyed father knew immediately it was Andrew.
"I thought, `It's him, my boy, my Andrew'," he told News Limited newspapers.
"He's got some sort of accent now, but he still speaks perfect English and he's got a strong little personality.
"It's my Andrew."
Mr Thompson quit his job to cycle 6500km across Europe searching for his son and publicising his disappearance.
Andrew, who is now in a Dutch childcare institution, came to the attention of Amsterdam police on September 5 after a tip-off from a family friend.
Ms Stratton was arrested the following day.
A team of Dutch psychologists prepared father and son for their emotional meeting and the 57-year-old said it was a nerve-racking wait to see Andrew.
"He was nervous, too, but he looked at me and gave a little smile straight away," Mr Thompson said.
"After all this time, I didn't know how he would react and what his mother has told him about me.
"So it could have been pretty bad. But it was fantastic."
The pair met in a small room filled with toys, and the two rekindled their relationship as they played together.
"He walked towards me and got close, then veered off and got some toys and asked me to play with him," Mr Thompson said. "We sat there playing a board game puzzle, and he slowly opened up a little as we played.
"I let him take control, and he really took the lead in how we spoke and what we spoke about."
Andrew didn't ask any questions about his former life in Australia or why he had not seen his father since he was three-and-a-half.
"I still don't feel like a dad, I'm a father but now I want to learn again to be a dad, to do the things that dads do."
Mr Thompson is waiting for Dutch childcare experts and psychologists to organise further meetings with Andrew.
The experts are taking a cautious approach because of the upheaval Andrew has endured in the past fortnight.
It is understood it could take months before Andrew is allowed to return to Australia with his father.