The Chelmsford-based company has been offered an all-cash deal at 275p per share, representing a premium of 48% on Friday's closing price.
The executive boards of both companies have agreed to the deal. e2v is now urging shareholders to vote in favour of the acquisition.
It is the latest UK firm to be bought by an American company following the significant drop in sterling since the EU referendum.
The pound has fallen by more than 16% against the US dollar since the Brexit vote, providing would-be American buyers with a potential discount through British acquisitions.
e2v chairman Neil Johnson said: "Teledyne has recognised the value inherent in our business and prospects by making a cash offer at an attractive premium to the share price.
"The board of e2v has also considered the merits of being part of a larger, complementary group with enhanced scale and a wider range of capabilities to service its key customers and management and employees having access to the opportunities available in a larger group."
Cantor Fitzgerald previously had a "buy" recommendation on e2v's stock, "based on a growing pipeline of opportunities, particularly in professional imaging, radiotherapy and the space exploration markets."
William Game, a general industrials research analyst at Cantor Fitzgerald, said: "Teledyne's board believes that there is a highly complementary fit between the two businesses and this should enable both companies to accelerate revenue growth across a range of multiple industrial markets."
e2v shares were up by around 87.38p at 272.88p in afternoon trading.