Miller had been on trial with the Bairns while negotiations were being held with the English Premier League club over a six-figure fee for Biabi.
The 32-year-old started out at Falkirk and will add to his 73 appearances after signing a "short-term deal".
Miller, capped three times, was released by Kilmarnock this summer.
He played 22 times, mainly as a substitute, for the Scottish Premiership side after signing a two-year deal after leaving Carlisle United last summer and scored once for the Ayrshire outfit.
Miller also numbers Bristol City, Hearts, Dundee United, Aberdeen, Middlesbrough, Notts County and Scunthorpe United among his former clubs.
The striker who scored 30 goals in his previous stint with Falkirk found the net again in last week's 3-3 Development League draw with Hibernian.
He will go straight into the Championship club's squad for Tuesday's Petrofac Training Cup visit by Peterhead.
Meanwhile, fellow striker Biabi has completed his switch to Swansea, signing a three-year contract with the English Premier League club.
The 19-year-old graduate of Falkirk's academy made 32 first-team appearances for the Bairns, mainly from the bench, scoring four times.
Former Scotland striker Lee Miller has returned to Falkirk after the Bairns completed the sale of teenager Botti Biabi to Swansea City.