Rebecca is currently in Rio covering the 2016 Olympic Games' swimming events for the BBC, and she was sent the short clip by her family, who are looking after Summer back in the UK.
The retired swimmer, who won two gold medals at London 2012, admitted the video made her teary-eyed before she counted down the days until they are reunited.
She captioned the footage "THIS", along with four red heart emojis. She added: "#missyou #3moresleeps #crying."
Sports star Rebecca and her estranged husband Harry Needs welcomed Summer into the world in June 2015. Sadly, the couple announced the end of their 18-month marriage in March this year.
In a statement, they said: "It's after much thought and sadness that we confirm our separation. It is on amicable terms and we still remain close friends.
"We move forward with respect for one another and our focus and commitment is on parenting our gorgeous daughter Summer. This will be our only comment on this private matter. Becky and Harry."
Rebecca is due to return home to England in the coming days, but she has been a huge hit with viewers. One replied to her video: "Best commentary team of the Olympics goes to the Swimming team." Another added: "@beckadlington just wanted to say I think you do an amazing job doing the coverage for the Olympics and make it very enjoyable to watch. You are the one that made me want to learn how to swim and now im in the pool every day improving my technique and recording new PBs!"
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