The Bourne Legacy is the fourth film in the series and sees Tony Gilroy take over the director's chair while Jeremy Renner plays new character Aaron Cross for the first time.
The movie took $40.3 million in the opening weekend to comfortably take the #1 spot and topple the Christopher Nolan directed movie.
The Campaign was also another new entry in at number two as Will Ferrell teams up with Zach Galifianakis in the comedy.
The movie took $27.4 million to also overtake The Dark Knight Rises but the Jay Roach directed film never came close to challenging The Bourne Legacy for the number one spot.
The Dark Knight Rises slip two places this week after spend three weeks at the top of the box office.
The movie became the second biggest grossing movie of 2012 last week and took a further $19.5 million over the weekend.
Hope Springs, which sees Meryl Streep team up with Tommy Lee Jones, was the third and final new entry inside the top ten this week at number four.
Diary of a Wimpy Kid: Dog Days was down two places this week to round off the top five.
Total Recall, a remake of the 1990 movie, was this week's biggest faller as it dropped four places from two to six.
Ice Age: Continental Drift was down three at seven while comedy Ted was a two place faller at number eight.
Step Up Revolution was down two at nine while The Amazing Spider Man was also a two place faller at number ten.
1. (-) The Bourne Legacy $40.3 million
2. (-) The Campaign $27.4 million
3. (1) The Dark Knight Rises $19.5 million
4. (-) Hope Springs $15.6 million
5. (3) Diary of a Wimpy Kid: Dog Days $8.2 million
6. (2) Total Recall $8.1 million
7. (4) Ice Age: Continental Drift $6.8 million
8. (6) Ted $3.3 million
9. (7) Step Up Revolution $2.9 million
10. (8) The Amazing Spider-Man $2.2 million