Rebirth unlocks at Level 50
gamestratwiki's beginner guide confirms Rebirth becomes available once your character reaches Level 50. No other level threshold has been reported by any source checked for this page.
The exact Rebirth bonus is not officially disclosed
None of the sources checked — gamestratwiki, Destructoid, or Pro Game Guides — publish a specific multiplier or stat bonus for completing Rebirth. Treat any specific percentage you see elsewhere as unverified until the game itself confirms it.
How to verify the bonus yourself
Since leveling's +1% Attack Damage per level is confirmed, you can isolate Rebirth's effect by noting your displayed Attack Damage right before hitting Level 50, rebirthing, and comparing the number afterward at the same level. That difference is the actual Rebirth bonus in your current version, which may change between updates.
Should you rush to Level 50?
Because the core loop already rewards you every time you die and revive, leveling to 50 happens naturally through normal play rather than requiring a special strategy, per gamestratwiki. No source checked reports a penalty for rebirthing later rather than immediately at Level 50.