In a letter to City, N.J.-based Knight, Getco said the acquisition would involve a two-step process in which 242 million new shares would be issued, followed by a tender offer for an additional 154 million shares.
Getco already owns about 31 percent of Knight's outstanding shares.
Getco, in a regulatory filing said that CEO Daniel Coleman would lead the new company, and Knight CEO Tom Joyce would become non-executive chairman.
In recent weeks, rivals Getco and Virtu Financial have each approached Knight about the possibility of purchasing the company and merging into it, according to people familiar with the matter.
Uncertainty has hung over Knight since an Aug. 1 trading glitch caused the company to take on a slew of unwanted positions in stocks, in both purchases and short sales. Knight's Joyce managed to sell off the erroneous purchases quickly, but was ultimately left holding $460 million in losses.
In the aftermath of the glitch, the Securities and Exchange Commission opened an investigation into what went wrong, and Knight was forced to take on a new group of investors to raise emergency financing.
Shares of Knight (NYSE: KCG) surged in pre-market trading following word of the offer.
-The Associated Press and CNBC's Kate Kelly contributed to this article