First off, I'll say this: I've got no doubt the looming 3 PM deadline helped spur that deal along mighty quickly, as a player with no leverage saw an improving offer and jumped on it before he was left with no long-term security beyond the 2012 season.
Let's hit the jump, and dig into the exact numbers of the contract.
Per Rotoworld, here's the contract breakdown:
7/16/2012: Signed a four-year, $30.4 million contract. The deal contains $17.1 million guaranteed, including a $4 million signing bonus, a $5 million first-year roster bonus, and all of Forte's first-year base salary. Forte is eligible for annual $100,000 workout bonuses in years two through four.
2012: $800,000 (+ $5 million roster bonus),
2013: $1.7 million (+ $2.5 million roster bonus due 3/31 + $500,000 in per-game roster bonuses),
2014: $5.5 million (+ $1 million in per-game roster bonuses),
2015: $6.65 million (+ $1.05 million in per-game roster bonuses),
2016: Free Agent
I spaced out the years so it might be easier to read/digest. Forte got a $4 million signing bonus, so that cap his is spread into all four seasons, at about a million per, so let's mentally add that into each total. That'll jump the 2012 cap hit up to all of about 6.8 million, about 900K short of what the franchise tag would hit at.
But it gets better. 2013 jumps to an overall cap hit of... 5.7 million? But that's lower! (Edit: As mentioned in the comments, Spotrac has Forte getting a 4 million roster bonus versus the 2.5, pushing the cap hit to 7.2.)
2014 goes to a cap hit of 7.5 million, which as of right now, the Bears have plenty of room to absorb, and in 2015, it reaches 8.7 million - but remember the old adage about how the final years of contracts in the NFL are never heard from and usually eliminated, either through extensions or cutting.
Now, some quick thoughts... The low salary in the first year of a contract like this normally isn't a big hit anyway - and in Forte's case, it's a raise over his 2011 salary. That being said, he picks up the signing bonus and just about picks up the roster bonus free and clear, so he gets about nine million in his pocket over the span of two months.
Second of all, it's a well-designed contract for the Bears. They pick up a little extra flexibility both in the remainder of 2012, in case someone they like slips through the tough cuts that inevitably come at the end of training camp (remember picking up Brandon Meriweather? Wasn't that fun, guys? Guys?). And they pick up some added flexibility in future years as well - they don't have to tag Forte next year, saving about two and a half million, and pending the TV deal cap bump, are well positioned to handle Forte's 8.7 if it comes to that.
So all in all, I think it's both a good deal for Forte and an excellent deal for the Bears. It definitely comes in below what Forte thought he was worth, but he takes home more cash than the franchise tag would have paid him in 2012, the cap hit to the Bears is lower than what the tag would have foisted upon them, and the Bears lock up a solid running back and a strong offensive cog for the forseeable future while affording them the flexibility to continue to build the roster.