Danaher's 89m offer for Linx, based in St Ives, Cambridgeshire, works out at 550p per share.
A deal became more likely after the Washington-based maker of environmental controls trumped a rival offer of 74.2m last week from Illinois Tools Works (ITW).
A spokesman for Linx said Danaher had 28 days to post the offer to shareholders and a deal could be struck less than a month later.
Linx produces ink-jet and laser printers for date-and-batch coding of packaging. Sales of kit like the Linx 4900 ink-jet and Xymark laser coder have helped build a turnover of around 52m and pre-tax profits of 5.6m.
The spokesman said last month's year-end results for Linx were its "best revised results and the firm was relatively upbeat".
Story by Jez Abbott