The deal, already approved by the Tyco and ADT boards, is a blow to Western Resources, a Kansas-based utility giant that had been struggling since last year to make ground with its $3.5bn (pounds 2.2bn) hostile bid.
Tyco, which makes a diversified range of products including packaging and medical goods, agreed to play the role of "white knight" by offering ADT shareholders $29 a share against the $22.50 put on the table by Western Resources.
Shares in ADT, the leading home-security firm in Britain and the US, jumped 15 per cent in early New York trading from a Friday close of $21.75.
The deal was welcomed by Mr Ashcroft, whose empire also includes car auction interests in Britain. "ADT's commercial and industrial businesses are an excellent fit with Tyco's Fire and Safety Services group," he said. "This merger will enhance ADT's ability to continue its growth, not only in North America and the United Kingdom, but in all parts of the world."
ADT's 230 offices in 10 countries will be merged with the 300 offices of Tyco's Fire and Safety unit in 50 countries. The current head of Tyco - which is unrelated to the Tyco toy company - Dennis Kozlowski, will remain chairman after the merger. The Tyco name will also be retained. Tyco is based in Exeter, New Hampshire. ADT has its operating home in Boca Raton, Florida.
Under the deal, which should be completed by 1 July, Tyco will end up owning 64 per cent of the shares of the new company while ADT shareholders will have 36 per cent. Among the latter may be thwarted Western Resources, which currently holds a 27 per cent stake in ADT. Western Resources had no comment yesterday.
The struggle over ADT started last summer when a takeover agreement was struck with Wayne Huizenga's fast-expanding Republic Industries. The deal collapsed when Republic's share price plunged.
Home security firms have become attractive targets because of the opportunities they offer to gain contact with house-holders.