The defender will get to work with the club's doctors and physios in the summer, and he may even join in training when he is fit again.
In a farewell interview with United's SUTV channel, Basham said: I'm leaving with the thought of what I've achieved and I'm overwhelmed. I couldn't imagine the promotions that we've had, the ups and some downs of course.
But there have been many ups and I've become a part of a family, of a true club and a club that I've adored playing for, for the last 10 years. I'm so proud to have been a Blade.
I think since I've been injured it has sunk in a lot more, because I always thought I was going to be still playing. But now that I've had time to reflect and look at things, there are definitely some proud moments in there. There's no anger at all in leaving Sheffield United.
I hope the club builds again and rises again, like it always does. I'm sure with the manager and the staff he's got here now, and the rebuild that's going to happen, that they can do it again. And I'll be hopefully in the stands to watch it."