From Openssl pkcs8 default format gives RSA PRIVATE KEY (migrated from Stack Overflow):
Perform pkcs8 with -topk8 to convert this key from traditional format to pkcs#8 format.
openssl pkcs8 -topk8 -inform pem -in file.key -outform pem -nocrypt -out file.pem
Above, traditional format is -----BEGIN RSA PRIVATE KEY-----
, and PKCS8 format is -----BEGIN PRIVATE KEY-----
.