The 22-year-old Croatian international was at St James' Park last week, but snubbed Newcastle's offer and signed for Spurs at the weekend in a deal which was believed to be in the region of £15million.
And Tottenham have now verified that they are set to pay Dinamo a fee of £16.6million in instalments over a period of four years, but Modric must still obtain a work permit before his six-year contract is finalised.