Scripps' channels include the Food Network and Travel Channel. The two companies are estimated to have 20% of ad-supported TV viewership in the US
The two said the deal would enable them to compete better with online options.
Firms such as Amazon and Netflix are increasing competition in the sector.
Discovery and Scripps are also grappling with changing models of distribution, as cable companies respond to falling subscriber numbers with their own online platforms and less expensive packages with fewer channels.
"We believe that by coming together with Scripps, we will create a stronger, more flexible and more dynamic media company with a global content engine that can be fully optimised and monetised across our combined networks, products and services in every country around the world," said Discovery chief executive David Zaslav.
The offer values Scripps stock at $90 per share, 34% higher than the price when reports of the deal first circulated earlier this month. The $14.6bn deal includes Discovery's assumption of $2.7bn in Scripps debt.
The companies said they expect to make $350m in savings through the combination, which is subject to regulatory review. The deal is expected to be completed by early 2018.
Discovery's channels also include Science, Turbo/Velocity and Eurosport. The company, which has its headquarters near Washington, DC, employed about 7,000 people at the end of 2016.
Scripps, based in Tennessee, owns international ventures such as UKTV, a commercial joint venture with BBC Worldwide and TVN, a premiere multi-platform provider of entertainment, lifestyle and news content in Poland.
Reports of a possible merger started circulating earlier this month, pushing up share values of both companies.
Scripps shares held steady after the firms announced the deal on Monday, rising 0.7% in opening trade. Shares of Discovery, which also reported quarterly earnings, fell nearly 7%.
Analysts at research firm Moffett Nathanson said the deal could lead to some benefits, but was unlikely to change the long-term challenges faced by the two firms.
"While there will likely be ample cost synergies, international revenue opportunities and improved relative scale, we don't think this merger will fundamentally alter the long-term prospects of these companies."
Discovery Communications, owner of the Discovery Channel and Animal Planet, is buying Scripps Networks for $14.6bn (Â£11.1bn) in a deal that combines two major US television companies.