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."

In an interview for June's edition of Empire magazine, Moore recalled his early meetings with 007 film director Guy Hamilton.
Moore said that while he would be playing the same character they wanted to avoid "any deliberate" comparisons.
The interview, one of a series in Empire on Bond, came ahead of new Bond film Skyfall.
Starring Daniel Craig as 007 and directed by Oscar-winner Sam Mendes, the latest movie in the franchise will be released in October.
Scenes have been shot in London, Turkey and the White Corries in Glencoe.
The filming in the Highlands in February reportedly involved a car chase featuring Aston Martin DB5s - the same car driven by Connery in Goldfinger and Thunderball.
Talking about his early discussions with Hamilton about taking over from Scottish actor Connery, Moore said: "We talked about my approach to the character.
"The thing he wanted to avoid was any deliberate comparison to Sean, apart from the fact I was playing the same character.
"So I was never saying 'Martini, shaken not stirred'."
In her interview with Empire, producer Barbara Broccoli recalls how Connery exploded the traditional image of a movie's leading man.
Ian Fleming's books about the secret agent were adapted for film by Broccoli's father Cubby Broccoli and Harry Saltzman.
She said: "The typical British leading man used to be Trevor Howard or Leslie Howard - very polite and your classic gentleman.
"I think the real genius of Cubby and Harry was the fact that they didn't pay any attention to the typical class structure and they took someone who was a very real person and put him into this suit."
The magazine tells of "unsung hero" Yat Malmgren, a Swedish dance teacher to whom Connery turned to help hone his movement and gestures.
It also tells of Dr No scriptwriter Terence Young introducing Connery to his Savile Row tailors and then telling the actor to sleep in the suits.
Empire said the idea was to give the character the look of a man who had an eye for finery, but was more caught up in "life and death than ironing shirts".
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.
[NEXT_CONCEPT]
Roger Moore has told how one of his first decisions before taking over the role of James Bond was not to use Sean Connery's famous phrase "shaken not stirred".