Thanks GetMem. Just to say your method works fine with BGRABitmap as well.
Simply replace:
Image1.Picture.LoadFromStream... with FBGRA.LoadFromStream... (where FBGRA is TBGRABitmap object).
Edit: if your base64 comes from a web page, remove the first text, else it will crash:
base64data.Replace('data:image/png;base64,', '')