Amazon founder Jeff Bezos and his wife are making their first major foray into politics with a $10 million contribution to a super PAC that aims to elect military veterans to Congress.

The contribution introduces Mr. Bezos, who also owns the Washington Post, to a class of political megadonors that includes Las Vegas casino magnate Sheldon Adelson and California billionaire Tom Steyer, who have each poured more than $100 million into elections over the past decade.

But unlike with Messrs. Adelson and Steyer, the Bezos contribution isn’t to a partisan political organization. Instead it is to With Honor Fund, a year-old super PAC that backs veterans of both major parties who are running for House seats. Federal Election Commission filings show the organization had raised $7 million between its launch last October and the end of July.

Rye Barcott, the founder of With Honor Fund, said the Bezoses shared his group’s goal of building a “cross-partisan coalition” of House members willing to work with the other party.

“They perceive themselves to be pretty nonpartisan,” Mr. Barcott said. “The idea of doing something different and disruptive appealed to them, along with our focus on values and integrity in our national discourse.”

A Bezos spokesman confirmed the contribution and said the Amazon chief executive and his wife, MacKenzie, declined to comment.

With Honor Fund is backing 33 House candidates now running—19 Democrats and 14 Republicans. Mr. Barcott said the PAC does “no screening for ideology,” but rather seeks out a “common bond of service and commitment to the country.”

In a New Hampshire House race, With Honor’s ads backing Democrat Maura Sullivan show President Trump’s face as it says she will back “affordable health care...no matter who stands in the way.But in an ad for Michael Waltz, the GOP nominee for a House seat in northeast Florida, With Honor says Mr. Waltz will “work with President Trump to fight for Florida’s conservative values.”

Mr. Barcott said With Honor Fund backs candidates who agree to its three-point pledge, which calls for integrity, civility and courage.

Other major With Honor contributors include Leslie Wexner, the CEO of the company that owns Victoria’s Secret, and his wife, Abigail Wexner, who gave a combined $2.8 million. Mr. Bezos’s parents gave the super PAC $2 million.

Mr. Bezos, whom Forbes magazine in March ranked as the world’s richest man with a net worth of more than $150 billion, has to this point not been an active campaign donor.

FEC data shows that since 2007 the couple has given $52,600 to federal candidates—$31,000 of that went to Democrats and $21,600 to Republicans.

They have also given $170,000 to PACs associated with Amazon and Blue Origin, a Bezos-owned aerospace manufacturer.”

In Washington state, where the Bezoses live, the couple gave $2.5 million to back a 2012 referendum to legalize same-sex marriage. Beyond that, they have given just $8,400 to state-level candidates.

Mr. Bezos joins a roster of American billionaires who have spent tens of millions of dollars backing candidates.

This year Mr. Adelson and his wife gave $55 million to the super PACs backing House and Senate Republicans. Richard Uihlein, an Illinois shipping magnate, has spent $31 million this year on federal candidates and PACs and millions more on state-level races.

Mr. Steyer, who advocates impeaching Mr. Trump, has spent $30 million so far on Democratic candidates and PACs.

And former New York City Mayor Michael Bloombergsignaled in June that he would spend $80 million to elect Democrats in 2018, but FEC records show he has given just $1 million so far. Bloomberg spokesman Howard Wolfson said Tuesday that Mr. Bloomberg still plans to spend to back Democrats.

Write to Reid J. Epstein at reid.epstein@wsj.com