Have you tried the ConsoleReporter?
jasmine.getEnv().addReporter(new jasmine.ConsoleReporter(console.log));
According to the code Jasmine has the ConsoleReporter class that executes a print function (in this case console.log) that should do what you need.
If all else fails you could just use this as a starting point to implement your own console.log reporter.
UPDATE
In newer versions of jasmine, ConsoleReporter was removed. You can either use the built-in jsApiReporter, or write your own (console) reporter, as shown in the following link: https://jasmine.github.io/tutorials/custom_reporter