Both advanced through to Sunday morning's finals by meeting the automatic qualifying mark of 21.35m with their second round throws.
Gill, competing in group A, threw bang on the qualifying mark to secure his place in the final.
Walsh meanwhile qualified with a throw of 21.48m.
Italy's Leonardi Fabbri was the top qualifier with a throw of 21.76m, while gold-medal favourite Ryan Crouser of the US placed third in his qualification group after heaving the shot 21.49m.
The men's shotput final will get underway on Sunday morning at 5.35am.
Here's what Walsh had to say in the mixed zone: "My first round throw was a little bit short and tight, so all I wanted to do (for the second round) was commit to the throw and stay long through it, and that's exactly what I managed to do on that second round throw.
"Today is all about qualifying, so I managed to tick that off, and now onto the final."
Asked how he would prepare for Sunday morning's final, Walsh said: "Some kai, some treatment, some rest. A little bit of a warm-down, but my warm down is a walk round the track once, and that's about it really."
The atmosphere was "amazing" at the Olympic stadium, he said: "I was saying to someone out there, my wife said to me, 'Imagine what little Tom would have made of all of this'.
"Sometimes we can kind of get a bit scared of [the big crowds and pressure] and back away, and I wanted to make a point of taking it all in and going, 'Wow this is amazing'."
