The deal comes amid a new wave of consolidation in the semiconductor industry that included Singapore-based chipmaker Broadcom Ltd unveiling a $117 billion bid to acquire U.S. rival Qualcomm Inc.
Aliso Viejo, California-based Microsemi supplies high-performance analog and mixed signal integrated circuits and semiconductors to the aerospace and defense, communications, data center and industrial sectors.
Microsemi, which has grown in the last few years through a wave of acquisitions, has said it wants to expand further in aerospace and defense.
Microchip currently gets about 2 percent of its annual sales from the aerospace and defense markets.
The deal would also strengthen Microchip's base in the computing and communications sectors, which together accounted for less than 15 percent of its full-year sales.
The transaction includes a $68.78 per share cash offer, representing a premium of about 7 percent to Microsemi's closing price on Thursday.
Shares of Microchip were up about 5 percent at $93.40 in extended trading, while that of Microsemi rose about 5 percent to $67.55, shy of the offer price.
Earlier this week, The Wall Street Journal reported that Arizona-based Microchip was in talks to buy Microsemi.
Microchip said on Thursday the deal, which is expected to close in the second quarter of 2018, would immediately add to its adjusted earnings per share.
The chipmaker expects an estimated savings of $300 million in the third year after the deal close.
J.P. Morgan, which is providing $5.6 billion in committed financing for the deal, was Microchip's financial adviser, and Qatalyst Partners advised Microsemi.
Microchip on Thursday also narrowed its net sales forecast for the fourth quarter ending March to a range of flat to down 2 percent, from up 1 percent to down 3 percent.
The company said it now expects adjusted earnings per share for the quarter to be at between $1.32 and $1.37, compared with $1.30 to $1.39 per share previously.