Indianapolis will give the veteran a two-year, $24-million deal, a source told ESPN's Adam Schefter.
Houston heads to Indy after an eight-year tenure with the Kansas City Chiefs that included a quartet of Pro Bowl selections. He was released March 10 due to schematic changes on the Chiefs' defense and his hefty salary.
The 30-year-old edge defender racked up 78.5 sacks over his Chiefs career, nine of which he recorded last season despite missing four games.
Houston will bolster an Indianapolis pass rush that tied for the 19th-most sacks in the NFL last year. Since 2016, he has the fourth-highest pressure percentage among edge rushers, according to Pro Football Focus.
The Colts entered free agency with more cap space than any other team in the NFL but were relatively quiet early on, with their lone splash being the addition of wide receiver Devin Funchess on a one-year contract.