It's WIF (Wallet Import Format), and AFAIK, vanitysearch doesn't have a converter command since it's already included in the result.

If you want to know how, it's not that complicated, you just need some tools for SHA256 computation (Hash online tool) and Base58 encoder/checker (Base58 online tool),
Then, follow these steps:

• 1. Get the private key hex,
  Sample: 4116A49CA05407397C159D9F8EFC32064E3165466173AA26D21DA11A169BF7FD
• 2. Insert 80 at the start of the prv key and 01 if you want the compressed prv key WIF (do not insert 01 if uncompressed).
  Sample Compressed: 804116A49CA05407397C159D9F8EFC32064E3165466173AA26D21DA11A169BF7FD01
  Sample Uncompressed: 804116A49CA05407397C159D9F8EFC32064E3165466173AA26D21DA11A169BF7FD
• 3. Get the SHA256 Hash of the string above (as HEX not text):
  Sample Compressed: 47aa53130b00c52fed1cf223a04bce7a2d083f111ed5b3dcb6a2a23f06dc3c78
  Sample Uncompressed: 1a75a1d066dcc407ac94a8e07042bb3fcf97f0c41b9d23c2ec9b54fc75b8e2c4
• 4. Get the SHA256 Hash of the SHA256 Hash above:
  Sample Compressed: 78a9182fdc5389e180d08702ac1ec0707221c861b08a7c0e3da56465c01104f9
  Sample Uncompressed: 7b376ba10130e9ae74f447847fbc5ae1c076d42efc932e8dc30ca64401835c8f
• 5. Get the first four bytes of the Double SHA256 hash from step4 (the first 8 characters), that'll be the 'Checksum':
  From Compressed: 78a9182f
  From Uncompressed: 7b376ba1
• 6. Then insert the result of step5 after the result of step2:
  Sample Compressed: 804116A49CA05407397C159D9F8EFC32064E3165466173AA26D21DA11A169BF7FD0178a9182f
  Sample Uncompressed: 804116A49CA05407397C159D9F8EFC32064E3165466173AA26D21DA11A169BF7FD7b376ba1
• 7. Encode to Base58 the strings above and you'll get the WIF format:
  Compressed WIF: KyQEYWYtkttfuaMGBqoBqtpkUJ4M8yHKVtQ3pBkXChBXbraGiS2z
  Uncompressed WIF: 5JJxBK2LRu5umY7rfFgTvfvsBGCBTGvYNx9Pqkfrtb2Un7BrosE

If you need to do this automatically, just paste it on bitaddress.org's "Wallet Details" link.