Electrical – I2C Communication between Arduino Uno and mbed

If they both use I2C then you can attach them both to the same two pins (SDA and SCL)

You select which one you wish to talk to by using it's address for the first byte of each command (which should be given in the documentation along with example communications) For example on page 16 of the datasheet for the BMP085 this is given as 0xEE (write) and 0xEF (read)
It looks like the first sensor has pullup resistors included which means you don't have to add them yourself.

I take it the Arduino Wire library is a software implementation of I2C (as opposed to a dedicated on board peripheral) If this is the case I imagine you can select which pins you want to use in the defines section. So in your case you would select A4 and A5 as SCL and SDA (which ever way round you want them)

The first link I looked at had various helpful links including quickstart guide, datasheet, wiring example, and an example Arduino sketch, so I'd probably start by following those. To keep it simple, I would try and get that sensor talking to the Arduino then add the other one.

I notice that the BMP085 runs from 3.3V, so you will need to use a 3.3V supply and disable the weak pullups to 5V in the Arduino wire library (see comments on product page) You can probably run the other sensor from 3.3V too but you would need to confirm this - it should work fine from 5V with logic high to 3.3V anyway if necessary.

Some folks are having a hard time visualizing things connected together, so here's a picture:

(Serving suggestion)

^{simulate this circuit – Schematic created using CircuitLab} I²C is a bus, so like-named signals are connected together. The addressing scheme allows the microcontroller to select which device it's talking to. On the Arduino, the 10kΩ pull-up resistors go to V_DD (Usually +5V or +3.3V).