You can import makehuman models directly into UE4 however if you want to retarget the Animation Starter Pack assets, the pose will never be quite right.

Follow this guide to remedy this.

If any stage is unclear to you, you can watch the youtube video.

Use makehuman nightly build, earlier versions do not contain the correct skeleton.

Feel free to play with the Gender, Muscle, Weight and Height sliders.

Your job will be easier if you turn on symmetry while editing the body.

For best results do not change proportions that will effect the skeleton.

In the Pose tab, select the Game Engine skeleton.

Export as .fbx with centimeter units. All other options remain the same.

Open blender, delete any objects in the scene and change a view to the text editor.

Create a new text file.

Paste in the python script from Github.

Import the makehuman model.

Scale it by 0.1.

With all makehuman objects selected, run the script.

For best results, weight paint the twist bones here. Only the left vertex groups are created, so that after weight painting the left side you can copy these vertex groups and mirror (topology mirror) them.

Export to .fbx with the pictured settings.

Use shift+click to select the Armat and Mesh options.

Import to UE4 with the pictured settings. Only the highlighted settings are important.

Open the new skeleton asset, and click 'Retarget Manager.'

In the Select Rig dropdown, click 'Select Humanoid Rig.'

Close the Retarget Manager. On the left, check the 'Show Advanced Options' checkbox.

We want all bones below pelvis to be in Skeleton mode. The easiest way to do this is right-click pelvis and choose 'Recursively Set Translation Skeleton.' Then set pelvis back to Animation.

NOTE: In UE4.14 and later this step is skipped.

Now open the UE4_Mannequin_Skeleton asset. Open the Retarget Manager and select the humanoid rig.

Finally right-click any Starter Pack animation and select 'Retarget Anim Assets->Duplicate Anim Assets and Retarget'

Choose your skeleton and retarget.

Congratulations!