The 27-year-old will sign a four-year deal at Craven Cottage with Marco Silva’s side delighted to secure their primary defensive target late in the transfer window.
Silva has long outlined the Belgium international as his favoured option after he told Leicester he wanted to leave following their shock relegation last season.
Juventus and Crystal Palace both explored a potential bid for Castagne but Fulham won the race having moved most decisively throughout the summer window.
Castagne is both versatile and experienced having played 112 times for Leicester in a variety of positions and has 33 caps for Belgium.
He is expected to be the first of several late window signings with another full-back, a midfielder, a winger and a striker also being considered.
Fulham remain interested in AC Milan’s Fode Ballo-Toure, Union Berlin’s Josip Juranovic and Southampton’s Kyle Walker-Peters before the transfer window closes on September 1.