Hi there
I had this EXACT problem with my baby until he was about 6 months old. I broke the habit through something I read in a book called the 'no-cry sleep solution' by Elaine Pantley. It didn't seem to take that long to fix and was a very untraumatic way of dealing with the problem for both of us...
Just as feeding has slowed and baby is suckling and not really feeding properly, kind of going to sleep on your breast - break him off. If he routes around, give it back to him and count for 10 or 20 (experiment to find the best intervel) and the break him off. keep doing it and eventually he should accept not falling asleep with it in his mouth. My Son (and another one featured in the book) even sometimes breaks himself off now when he's done. He will wimper a little bit sometimes if he's grumpy but a wimper will be all that it is.
At his bedttime feed, if he doesn't break himself off and he stops feeding properly and is just suckling I break him off. I sit back in the chair next to his cot and he lays lack with me and goes to sleep. I sing a few lullabies but then its just darkness and cuddles that seem to do it. I used to try and put him down when he was sleepy but now I just pop him in his cot and he rolls over onto his tummy to go to sleep. I usually hover around the cot for a moment or two and if he trys to get up, gently rub his back until he goes to sleep again.
This is part of his routine which is...
6.30/7ish bath
Changed for bed
Into nursery and feed with small light on
turn light off, afew lullabies and lay him on me in the dark till he gets sleepy.
In the day, he has a little nap routine which envolves reading some books in the chair next toi his bed followed by drawing the curtains and the same, lay him on me on the chair type thing.
I know that isn't the ideal 'baby falling asleep on his own' thing which most books and health visitors and mothers of better sleepers tell us to aspire too, but it works for us and it works for him. He will normally go about 5 hours or more, wake up once and then I bring him into bed with us where apart from the odd grizzle, he'll sleep through till morning.
Basically cuddles in a dark quite room have replaced the suckling.
Good Luck!!!