Palace's offer of £35m has been accepted by Spurs, with Johnson agreeing to the move on Thursday,
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The Wales international had offers from other Premier League clubs, but has agreed to remain in London and move to the Eagles.
BBC Sport says Johnson spoke with Palace manager Oliver Glasner yesterday the Eagles' 1-1 draw with Fulham in the evening.
Glasner aims to include Johnson in his squad for Sunday's clash with Newcastle.
Johnson is set to leave Tottenham having been their top scorer last season with 18 goals.