He said: "She would have loved this thing".
"Not only did it give us a focal point for our Get Together, it also means that staff can use it for lunch breaks which is good for their wellbeing, as it gets them away from their ward or computer".
Mrs Leadbeater said the anniversary of Mrs Cox's death would be "difficult" for the family but they were attending a number of community events in her honour.
Kim Leadbeater, Mrs Cox's sister, has thrown herself into organising the Great Get Together, but said she is aware there are still hard roads ahead.
Ms Sturgeon said: "Brendan Cox, Jo's husband, and the Jo Cox Foundation have to their great credit been really focused on trying to celebrate Jo's memory by getting people to focus on what unites us, not what divides us".
The life of the 41-year-old is being celebrated one year on in more than 100,000 events across the country, collectively named The Great Get Together. We've been awed by it.
"We need to stand together and show the people who want to divide us that we are united". A desire for unity and togetherness rather than the divisiveness of politics and the public debate in recent years.
"Jo's killing was an attack on democracy which shook the world". "So it's not as if today is actually very different for us in lots of ways".
Head to The Great Get Together's website for more info.
She said: "It's what Jo would have wanted".
Ms Sturgeon said: "I remember vividly as everybody does the sheer sense of shock a year ago when the news came through that an MP had been attacked, then a bit later on the awful news that she had been murdered".
In Scotland, First Minister Nicola Strugeon spoke of her shock at hearing news of Mrs Cox's brutal murder at the hands of Neo-Nazi Thomas Mair outside of a political surgery.
"If you think about things that hold us together, those really British values, whether it's values of equality or the way we all believe the fact the weather is terrible and we all like tea, these are more important than partisan politics and things that divide us".