The 30-year-old Republic of Ireland international has fallen out of favour at Ewood Park under new manager Steve Kean and has been at Portman Road since Tuesday completing the paperwork.
Andrews said: "Blackburn told me I could go out on loan and my agent started chatting to a few clubs, but it has been a little drawn-out and not as easy as we all would have liked.
"It is one of those things. Football is a horrible business at times and if your face doesn't fit, you have to move on. Thankfully I am at a place now where my face is fitting and I hope to fit in very well."