Dichio, who arrived on loan in the middle of January, has made an explosive start to his Lions' career, scoring five goals in three games before last night's FA Cup tie.
Millwall have agreed an initial fee of £500,000, which could rise to £675,000 if The Lions are promoted to the Premiership this season. The Baggies are guaranteed £200,000 upfront with a further £300,000 related to appearances.
The 29-year-old front man, who had his loan spell extended by West Brom as a favour to the club so he could play in last night's FA Cup tie, will have a medical today and is expected to sign this afternoon.
Lions chairman Theo Paphitis said: "Danny has done a fantastic job for us over the past month. Dennis and Ray were very keen to sign him permanently, and we have worked hard to make that possible.
"With the FA Cup Fifth Round tie against Burnley to look forward to on Saturday, and the Play-Offs still a realistic goal, bringing Danny in is a demonstration of our ambition and our ongoing commitment to bringing further success to Millwall Football Club."