The world of advertising has long been spurred on by competitors: Coke and Pepsi.  Ford and General Motors.  Apple and Microsoft. Now a different sort of struggle between two arch-rivals has the potential to change direction on Madison Avenue.

ComScore and Rentrak, two companies that specialize in the measurement of media consumption, have merged, forming a company that is likely to vie with Nielsen to offer data that can form the backbone of deals struck between media outlets and their advertisers. The two outlets gained shareholder approval late last week and officially completed their transaction quickly thereafter, executives said.

The deal folds Rentrak, which measures video-on-demand, movie box-office and set-top box data that tell how people watch TV, within ComScore, which measures consumer web activity. Executives from the company said they will move quickly to offer advertisers a way to gauge how viewers consume video entertainment, no matter whether they use a movie screen, TV, desktop computer or mobile device.

“We are going to be establishing new currencies for understanding the consumer’s multi-screen behavior,” said Bill Livek, vice chairman and president of ComScore, in an interview. Both he and Serge Matta, ComScore’s chief executive, said they expected to offer new measurement products quickly and to have their data play a role in this year’s “upfront” marketplace, where U.S. TV networks try to sell the bulk of their advertising for the coming programming season.

In the United States, ComScore will measure behavior on more than 260 million desktop screens, 160 million mobile phone screens, 95 million tablet screens, 40 million television screens, 120 million video-on-demand screens, and 40,000 movie theater screens representing well over a hundred million moviegoers, according to the company.

The two join forces after media companies have articulated a new desire for new measurement options as consumers move from TV screens to everything from streaming video to mobile apps. Philippe Dauman, the chief executive of Viacom, which has seen ratings for cable networks like MTV and Comedy Central tumble, has made it clear he expects that company to generate significantly more advertising revenue from deals that are not based on Nielsen ratings.

Nielsen is also attempting to find new ways to evaluate today’s very complex audience. The media-measurement company is promoting what it calls a “total audience” measure that it thinks will help media companies count much of the audience that consumes video in new ways that are not always evaluated by the system that has for decades been used to establish ad deals between TV networks and their sponsors.

“We don’t think we are competitive” with Nielsen, said Livek. “It’s sort of like, was the iPhone competing with the flip phone of a generation ago?”

There are some complexities that might give some customers pause. WPP, the large U.K.-based advertising conglomerate has been an investor in both Rentrak and ComScore, and will own up to 19.9% of the new merged firm. Nielsen could suggest to customers that ComScore is backed by a company that controls one of the world’s largest media-advisory agencies, GroupM, and therefore is not an independent arbiter. Sir Martin Sorrell, WPP’s chief executive, has been vocal about his desire to create a system for measuring media consumption that would provide an alternate to Nielsen.

WPP is to be a passive investor in ComScore, and will not hold a board seat. ComScore and Rentrak already do business with a host of companies not owned by WPP, and will continue to do so.

To measure media activity properly, “you have to include all screens, all the big ones: TV, VOD, DVR, timeshifting, digital, mobile, from over the top to over the air,” said Matta.” TV networks and advertisers can determine for themselves which company offers the best yardstick for a new era.