McColgan won gold at the Games in Birmingham in a record time of 30:48:60 to match her mother Liz McColgan’s gold at the 1986 Games in Edinburgh. It is her first major title.
Ms Sturgeon tweeted: “What an absolutely amazing night for Team Scotland – congratulations to all our medal winners so far in these Commonwealth Games.
“Every medal is special, but what a tear in the eye to see Eilish Mccolgan match her mum’s 1986 gold.”
Scottish Labour leader Anas Sarwar said: “Incredible! What a story!”
Channel 5 newsreader Dan Walker said his “whole family were screaming” for the last 600 metres.
Wrapped in a saltire, McColgan shared the emotional moment with her mother and her partner who were cheering her on from the stands in Birmingham.
Speaking to the BBC afterwards, she said: “It’s just been such an up and down year with Covid, initially, then another illness and a couple of niggles at the wrong time… but I honestly couldn’t have asked for any more tonight to have my family here.
“The crowd, in that last 200 metres, I can’t even explain it. It was vibrating through my whole body.
“I’ve never sprinted like that in my entire life. Without the crowd, I wouldn’t have finished like that. I just wanted it so bad.
To witness your daughter winning is just amazing and to win it in the same event I won it in
“It’s just an absolute dream.”
Liz McColgan joined her daughter and said: “For me as a mother, not even as just a coach, to witness your daughter winning is just amazing and to win it in the same event I won it in.
“She’s just ran the race I always knew she was capable of winning. It was amazing to watch, it was very nerve-racking to watch. It’s been a long time coming and she put it together tonight and I’m just really, really pleased.”
Team Scotland won three other gold medals on Wednesday: Duncan Ross won his fifth medal for the men’s 200-metre medley, Sarah Adlington for the 78kg and higher women’s judo, and Rosemary Lenton and Pauline Wilson for the women’s para lawn bowls.