How can I have Twitter Tweets show up on LinkedIn?

The reason you haven’t been able to find a third party service that offers this Twitter –> LinkedIn connection is because it’s not a third party solution, it’s actually something that’s built in to LinkedIn.
However, before I show you how to set things up I have to offer a bit of a sermon: I think that LinkedIn has artificially created traffic and activity by doing this and it’s rather broken. Why? Because when I go to LinkedIn I am only interested in career-related updates from my connections, whereas on Twitter I expect the whole schmeer, from location updates to what they’re eating for lunch, their thoughts on a new TV show or movie, etc. They’re not the same thing, they have different communities and the community members have different expectations of what’s to be shared.
On LinkedIn I have quickly learned to ignore the status updates because on any given moment every one of them will be republished tweets from a tiny subset of my connections, pushing updates from everyone else off the screen and sharing boring things that if I wanted to know about, I’d get by following them on Twitter.
Make sense?
Fortunately, there’s a way that you can find a middle ground, as I’ll explain after I show you how to set things up.

To start, click on “Settings” on the top right of your LinkedIn pages. There are a lot of different choices at this point, so you’ll want to scroll down and find the following…

Click on “Twitter Settings” and you’ll see that it’s pretty straightforward now that Twitter is using OAuth as a way to enable apps to access twitterstreams:

No surprise, click on “Add your Twitter account” and it actually jumps to Twitter. If you haven’t logged in to Twitter at this point, you’ll need to log in. If not, the next thing you’ll see is an OAuth Allow Access prompt:

You sure you want to do this? Click on “Allow” and after a few seconds of negotiating back and forth behind the scenes, you’ll find yourself back on LinkedIn and able to configure your Twitter account as desired:

Here’s where you can be savvy to the differences between your LinkedIn connections and Twitter followers: check on “Share only tweets that contain #in”, as I have done. Now the vast majority of your twitter updates will not bother your LinkedIn associates. It’s only those that actually contain the hashtag #in that show up (with the hashtag stripped out, conveniently).
A good solution! Now, be careful out there…